raw/output.csv

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\triangle RST \cong \triangle XYZ. Find y.,"[Congruent(Triangle(R,S,T),Triangle(X,Y,Z))]. [Find(y)]."
Use parallelogram MNPR to find y.,"Use [Parallelogram(M,N,P,R)] to [Find(y)]."
Let JK be the median of ABTQ. Find JK.,"Let [IsMedianOf(Line(J,K),Quadrilateral(A,B,T,Q))]. [Find(LengthOf(Line(J,K)))]."
Find m \angle Z in the trapezoid.,[Find(MeasureOf(Angle(Z)))] in [Trapezoid($)].
Find y.,[Find(y)].
Find the perimeter of the triangle. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Triangle($)))]. Round to nearest tenth if necessary.
Find the measure of \angle T to the nearest tenth.,[Find(MeasureOf(Angle(T)))] to nearest tenth.
Find x.,[Find(x)].
"In \odot K, MN = 16 and m \widehat MN = 98. Find the measure of LN. Round to the nearest hundredth.","In [Circle(K)], [Equals(LengthOf(Line(M,N)),16)] and [Equals(MeasureOf(Arc(M,N)),98)] [Find(LengthOf(Line(L,N)))]. Round to nearest hundredth."
Find x. Assume that any segment that appears to be tangent is tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find m \angle 4.,[Find(MeasureOf(Angle(4)))].
"In \odot X, AB = 30, CD = 30, and m \widehat CZ = 40. Find m \widehat AB.","In [Circle(X)], [Equals(LengthOf(Line(A,B)),30)] [Equals(LengthOf(Line(C,D)),30)] and [Equals(MeasureOf(Arc(C,Z)),40)] [Find(MeasureOf(Arc(A,B)))]."
Find x.,[Find(x)].
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
Find x.,[Find(x)].
Find y.,[Find(y)].
"If AD = 27, AB = 8, and AE = 12, find BC.","If [Equals(LengthOf(Line(A,D)),27)] [Equals(LengthOf(Line(A,B)),8)] and [Equals(LengthOf(Line(A,E)),12)] [Find(LengthOf(Line(B,C)))]."
"parallelogram MNPQ with m \angle M = 10x and m \angle N = 20x, find \angle Q.","[Parallelogram(M,N,P,Q)] with [Equals(MeasureOf(Angle(M)),10x)] and [Equals(MeasureOf(Angle(N)),20x)] [Find(MeasureOf(Angle(Q)))]."
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
Find \sin x.,[Find(SinOf(x))].
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
"In the figure, m \angle 4 = 101. Find the measure of \angle 5.",", [Equals(MeasureOf(Angle(4)),101)] [Find(MeasureOf(Angle(5)))]."
Find the area of the shaded region. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth.
Find RS.,"[Find(LengthOf(Line(R,S)))]."
Use parallelogram WXYZ to find m \angle WZY.,"Use [Parallelogram(W,X,Y,Z)] to [Find(MeasureOf(Angle(W,Z,Y)))]."
Find x.,[Find(x)].
Find y.,[Find(y)].
"In H, the diameter is 18, LM = 12, and m \widehat LM = 84. Find m \widehat LK."," [Circle(H)], [Equals(DiameterOf(Circle(H)),18)] [Equals(LengthOf(Line(L,M)),12)] and [Equals(MeasureOf(Arc(L,M)),84)] [Find(MeasureOf(Arc(L,K)))]."
Find x so that m \parallel n.,"[Find(x)] so [Parallel(Line(m),Line(n))]."
Find x. Round to the nearest degree.,[Find(x)]. Round to nearest degree.
"For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure.","[Similar(Shape($1),Shape($2))], to [Find(ScaleFactorOf(Blue(Shape($)),Green(Shape($))))]."
Find x.,[Find(x)].
"m \angle 11 = 4x, m \angle 12 = 2x-6. Find the measure of \angle 11.","[Equals(MeasureOf(Angle(11)),4x)] [Equals(MeasureOf(Angle(12)),2x-6)] [Find(MeasureOf(Angle(11)))]."
"In rhombus ABCD, AB = 2x+3 and BC = 5x. Find x.","In [Rhombus(A,B,C,D)], [Equals(LengthOf(Line(A,B)),2x+3)] and [Equals(LengthOf(Line(B,C)),5x)] [Find(x)]."
Find the length of \widehat AB. Round to the nearest hundredth.,"[Find(LengthOf(Arc(A,B)))]. Round to nearest hundredth."
"For trapezoid QRTU, V and S are midpoints of the legs. If QR = 2 and VS = 7, find UT.","[Trapezoid(Q,R,T,U)], [IsMidpointOf(Point(V),LegOf(Trapezoid(Q,R,T,U)))], [IsMidpointOf(Point(S),LegOf(Trapezoid(Q,R,T,U)))],. If [Equals(LengthOf(Line(Q,R)),2)] and [Equals(LengthOf(Line(V,S)),7)] [Find(LengthOf(Line(U,T)))]."
Find x.,[Find(x)].
Find x in the figure.,[Find(x)].
Find x.,[Find(x)].
Find the perimeter of \parallelogram JKLM.,"[Find(PerimeterOf(Parallelogram(J,K,L,M)))]."
Find x.,[Find(x)].
Find m \angle MNP.,"[Find(MeasureOf(Angle(M,N,P)))]."
"Find x so that GJ \parallel FK. GF = 12, HG = 6, HJ = 8, JK = x-4.","[Find(x)] so [Parallel(Line(G,J),Line(F,K))]. [Equals(LengthOf(Line(G,F)),12)] [Equals(LengthOf(Line(H,G)),6)] [Equals(LengthOf(Line(H,J)),8)] [Equals(LengthOf(Line(J,K)),x-4)]."
Use parallelogram NQRM to find w.,"Use [Parallelogram(N,Q,R,M)] to [Find(w)]."
Find x.,[Find(x)].
Find x.,[Find(x)].
Find the area of the shaded sector. Round to the nearest tenth.,[Find(AreaOf(Shaded(Sector($))))]. Round to nearest tenth.
Find the perimeter of trapezoid PQRS.,"[Find(PerimeterOf(Trapezoid(P,Q,R,S)))]."
Find y in the figure.,[Find(y)].
WXYZ is a parallelogram. Find m \angle YZW.," [Parallelogram(W,X,Y,Z)]. [Find(MeasureOf(Angle(Y,Z,W)))]."
Find the perimeter of \triangle DEF if \triangle DEF \sim \triangle GFH.,"[Find(PerimeterOf(Triangle(D,E,F)))] if [Similar(Triangle(D,E,F),Triangle(G,F,H))]."
"In the figure, m \angle 1 = 3a+40, m \angle 2 = 2a+25, and m \angle 3 = 5b-26. Find a.",", [Equals(MeasureOf(Angle(1)),3a+40)] [Equals(MeasureOf(Angle(2)),2a+25)] and [Equals(MeasureOf(Angle(3)),5b-26)] [Find(a)]."
Find the measure of \angle 1 if m \angle DGF = 53 and m \angle AGC = 40.,"[Find(MeasureOf(Angle(1)))] if [Equals(MeasureOf(Angle(D,G,F)),53)] and [Equals(MeasureOf(Angle(A,G,C)),40)]."
EC and AB are diameters of \odot O. Find its measure of \widehat ACE.,"[IsDiameterOf(Line(E,C),Circle(O))], [IsDiameterOf(Line(A,B),Circle(O))]. [Find(MeasureOf(Arc(A,C,E)))]."
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
P is the incenter of \triangle AEC. Find m \angle DAC.,"[IsIncenterOf(Point(P),Triangle(A,E,C))]. [Find(MeasureOf(Angle(D,A,C)))]."
"Quadrilateral ABCD is a rhombus. If AB = 14, find BC."," [Rhombus(A,B,C,D)]. If [Equals(LengthOf(Line(A,B)),14)] [Find(LengthOf(Line(B,C)))]."
Find the measure of \angle 5 if m \angle 4 = m \angle 5.,"[Find(MeasureOf(Angle(5)))] if [Equals(MeasureOf(Angle(4)),MeasureOf(Angle(5)))]."
"In the figure, m \angle 1 = 53. Find the measure of \angle 3.",", [Equals(MeasureOf(Angle(1)),53)] [Find(MeasureOf(Angle(3)))]."
Find z.,[Find(z)].
"Find a if c = 8, b = 10, and m \angle A = 60.","[Find(a)] if [Equals(c,8)] [Equals(b,10)] and [Equals(MeasureOf(Angle(A)),60)]."
"In \odot F, AB \cong BC, DF = 3x-7, and FE = x+9. What is x?","In [Circle(F)], [Equals(LengthOf(Line(A,B)),Line(B,C))], [Equals(LengthOf(Line(D,F)),3x-7)] and [Equals(LengthOf(Line(F,E)),x+9)] [Find(x)]?"
Find y.,[Find(y)].
"m \angle 2 = 2x, m \angle 3 = x. Find m \angle 1.","[Equals(MeasureOf(Angle(2)),2x)] [Equals(MeasureOf(Angle(3)),x)] [Find(MeasureOf(Angle(1)))]."
AD and CG are diameters of \odot B. Find m \widehat CGD.,"[IsDiameterOf(Line(A,D),Circle(B))], [IsDiameterOf(Line(C,G),Circle(B))]. [Find(MeasureOf(Arc(C,G,D)))]."
Find x.,[Find(x)].
Find x.,[Find(x)].
"Find the perimeter of the \triangle ABC, if \triangle ABC \sim \triangle CBD, AD = 5, CD = 12, and BC = 31.2.","[Find(PerimeterOf(Triangle(A,B,C)))], if [Similar(Triangle(A,B,C),Triangle(C,B,D))], [Equals(LengthOf(Line(A,D)),5)] [Equals(LengthOf(Line(C,D)),12)] and [Equals(LengthOf(Line(B,C)),31.2)]."
Find the measure of \angle 2.,[Find(MeasureOf(Angle(2)))].
Find x to the nearest tenth.,[Find(x)] to nearest tenth.
"\triangle EFG is equilateral, and EH bisects \angle E. Find x.","[Equilateral(Triangle(E,F,G))] and [BisectsAngle(Line(E,H),Angle(E))]. [Find(x)]."
Find m \angle 4.,[Find(MeasureOf(Angle(4)))].
Find y in \triangle PQR.,"[Find(y)] in [Triangle(P,Q,R)]."
Find x.,[Find(x)].
Find m \angle U.,[Find(MeasureOf(Angle(U)))].
Find the area of the triangle. Round to the nearest tenth if necessary.,[Find(AreaOf(Triangle($)))]. Round to nearest tenth if necessary.
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Find x.,[Find(x)].
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
Find x.,[Find(x)].
Find x.,[Find(x)].
What is m \angle EFG?,"[Find(MeasureOf(Angle(E,F,G)))]?"
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
Find x.,[Find(x)].
"In the figure, m \angle 2 = 110 and m \angle 12 = 55. Find the measure of \angle 2.",", [Equals(MeasureOf(Angle(2)),110)] and [Equals(MeasureOf(Angle(12)),55)] [Find(MeasureOf(Angle(2)))]."
"MNQR is a rectangle. If NR = 2x+10 and NP = 2x-30, find MP."," [Rectangle(M,N,Q,R)]. If [Equals(LengthOf(Line(N,R)),2x+10)] and [Equals(LengthOf(Line(N,P)),2x-30)] [Find(LengthOf(Line(M,P)))]."
"For the pair of similar figures, find the area of the green figure.","[Similar(Shape($1),Shape($2))], [Find(AreaOf(Green(Shape($))))]."
Find x.,[Find(x)].
"In the figure, m \angle 12 = 64. Find the measure of \angle 11.",", [Equals(MeasureOf(Angle(12)),64)] [Find(MeasureOf(Angle(11)))]."
Find BD.,"[Find(LengthOf(Line(B,D)))]."
"m is the perpendicular bisector of XZ, WZ = 4a-15 and WZ = a+12. Find WX.","[IsPerpendicularBisectorOf(Line(m),Line(X,Z))], [Equals(LengthOf(Line(W,Z)),4a-15)] and [Equals(LengthOf(Line(W,Z)),a+12)] [Find(LengthOf(Line(W,X)))]."
Find x.,[Find(x)].
Find the angle measure of \angle 2.,[Find(MeasureOf(Angle(2)))].
Find m \angle A.,[Find(MeasureOf(Angle(A)))].
Find m \widehat PO.,"[Find(MeasureOf(Arc(P,O)))]."
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Find the area of the kite.,[Find(AreaOf(Kite($)))].
AD and CG are diameters of \odot B. Find m \widehat ACF.,"[IsDiameterOf(Line(A,D),Circle(B))], [IsDiameterOf(Line(C,G),Circle(B))]. [Find(MeasureOf(Arc(A,C,F)))]."
Find the measure of \angle R to the nearest tenth.,[Find(MeasureOf(Angle(R)))] to nearest tenth.
Find y.,[Find(y)].
Find the area of the shaded sector. Round to the nearest tenth.,[Find(AreaOf(Shaded(Sector($))))]. Round to nearest tenth.
Find m \angle JKL.,"[Find(MeasureOf(Angle(J,K,L)))]."
"If b = 18, find c.","If [Equals(b,18)] [Find(c)]."
Find x.,[Find(x)].
"In \triangle ACE, P is the centroid. PF = 6 and AD = 15. Find PC."," [Triangle(A,C,E)], [IsCentroidOf(Point(P),Triangle(A,C,E))]. [Equals(LengthOf(Line(P,F)),6)] and [Equals(LengthOf(Line(A,D)),15)] [Find(LengthOf(Line(P,C)))]."
Equilateral pentagon PQRST is inscribed in \odot U. Find m \angle PTS.,"[InscribedIn(Equilateral(Pentagon(P,Q,R,S,T)),Circle(U))]. [Find(MeasureOf(Angle(P,T,S)))]."
"For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure.","[Similar(Shape($1),Shape($2))], to [Find(ScaleFactorOf(Blue(Shape($)),Green(Shape($))))]."
"A plane travels from Des Moines to Phoenix, on to Atlanta, and back to Des Moines, as shown below. Find the distance in miles from Des Moines to Phoenix if the total trip was 3482 miles.","A plane travels from Des Moines to Phoenix, on to Atlanta and back to Des Moines,. Find distance in from Des Moines to Phoenix if trip was 3482."
PM is a diameter of \odot R. Find m \widehat MQ.,"[IsDiameterOf(Line(P,M),Circle(R))]. [Find(MeasureOf(Arc(M,Q)))]."
Find y.,[Find(y)].
Find the perimeter of the figure. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Shape($)))]. Round to nearest tenth if necessary.
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
"For trapezoid QRTU, V and S are midpoints of the legs. If RQ = 5 and VS = 11, find UT.","[Trapezoid(Q,R,T,U)], [IsMidpointOf(Point(V),LegOf(Trapezoid(Q,R,T,U)))], [IsMidpointOf(Point(S),LegOf(Trapezoid(Q,R,T,U)))],. If [Equals(LengthOf(Line(R,Q)),5)] and [Equals(LengthOf(Line(V,S)),11)] [Find(LengthOf(Line(U,T)))]."
"If FK = 3x-1, KG = 4y+3, JK = 6y-2, and KH = 2x+3, find x so that the quadrilateral is a parallelogram.","If [Equals(LengthOf(Line(F,K)),3x-1)] [Equals(LengthOf(Line(K,G)),4y+3)] [Equals(LengthOf(Line(J,K)),6y-2)] and [Equals(LengthOf(Line(K,H)),2x+3)] [Find(x)] so [Parallelogram($)]"
Find x. Round side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
"In the figure, m \angle 4 = 104, m \angle 14 = 118. Find the measure of \angle 10.",", [Equals(MeasureOf(Angle(4)),104)] [Equals(MeasureOf(Angle(14)),118)] [Find(MeasureOf(Angle(10)))]."
Find x in the figure.,[Find(x)].
Find \cos A.,[Find(CosOf(Angle(A)))].
Find \angle 8.,[Find(MeasureOf(Angle(8)))].
Find the length of XY.,"[Find(LengthOf(Line(X,Y)))]."
\triangle RST \cong \triangle VUT. Find x.,"[Congruent(Triangle(R,S,T),Triangle(V,U,T))]. [Find(x)]."
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Polygon BCDE \cong polygon RSTU. Find x.,"[Congruent(Quadrilateral(B,C,D,E),Quadrilateral(R,S,T,U))]. [Find(x)]."
Find m \angle B.,[Find(MeasureOf(Angle(B)))].
WXYZ is a square. If WT = 3. Find XY.," [Square(W,X,Y,Z)]. If [Equals(LengthOf(Line(W,T)),3)] [Find(LengthOf(Line(X,Y)))]."
"In the figure, m \angle 1 = 4p+15, m \angle 3 = 3p-10 and m \angle 4 = 6r+5. Find the value of r.",", [Equals(MeasureOf(Angle(1)),4p+15)] [Equals(MeasureOf(Angle(3)),3p-10)] and [Equals(MeasureOf(Angle(4)),6r+5)] [Find(r)]."
"According to the Perpendicular Bisector Theorem, what is the length of segment AB below?","[UseTheorem(Perpendicular_Bisector_Theorem)], [Find(LengthOf(Line(A,B)))]?"
"In the figure, m \angle 8 = 96 and m \angle 12 = 42. Find the measure of \angle 6.",", [Equals(MeasureOf(Angle(8)),96)] and [Equals(MeasureOf(Angle(12)),42)] [Find(MeasureOf(Angle(6)))]."
"In the figure, m \angle 11 = 62 and m \angle 14 = 38. Find the measure of \angle 12.",", [Equals(MeasureOf(Angle(11)),62)] and [Equals(MeasureOf(Angle(14)),38)] [Find(MeasureOf(Angle(12)))]."
find \cos S.,[Find(CosOf(Angle(S)))].
"In \odot A, WX = XY = 22. Find AB.","In [Circle(A)], [Equals(LengthOf(Line(W,X)),22)] [Equals(LengthOf(Line(X,Y)),22)] [Find(LengthOf(Line(A,B)))]."
Find y.,[Find(y)].
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Find the perimeter of the parallelogram.,[Find(PerimeterOf(Parallelogram($)))].
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
"If b = 3, find c.","If [Equals(b,3)] [Find(c)]."
What is the area of the sector?,[Find(AreaOf(Sector($)))]?
Find the measure of \angle 1.,[Find(MeasureOf(Angle(1)))].
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Find JK.,"[Find(LengthOf(Line(J,K)))]."
Find y.,[Find(y)].
Find x.,[Find(x)].
"In rhombus ABCD, m \angle DAB = 2, m \angle ADC and CB = 6. Find DA.","In [Rhombus(A,B,C,D)], [Equals(MeasureOf(Angle(D,A,B)),2)] [MeasureOf(Angle(A,D,C))] and [Equals(LengthOf(Line(C,B)),6)] [Find(LengthOf(Line(D,A)))]."
Find x.,[Find(x)].
"a = 14, b = 48, and c = 50, find \tan B.","[Equals(a,14)] [Equals(b,48)] and [Equals(c,50)] [Find(TanOf(Angle(B)))]."
"Find the area of the shaded sector. Round to the nearest tenth, if necessary.","[Find(AreaOf(Shaded(Sector($))))]. Round to nearest tenth, if necessary."
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
find \sin R.,[Find(SinOf(Angle(R)))].
Find y.,[Find(y)].
Find y.,[Find(y)].
Find x.,[Find(x)].
Find x so that m \parallel n.,"[Find(x)] so [Parallel(Line(m),Line(n))]."
Quadrilateral ABCD is a rectangle. Find y.," [Rectangle(A,B,C,D)]. [Find(y)]."
Find y.,[Find(y)].
Find the perimeter of quadrilateral ABCD.,"[Find(PerimeterOf(Quadrilateral(A,B,C,D)))]."
Find m \angle Y.,[Find(MeasureOf(Angle(Y)))].
Find the exact circumference of the circle.,[Find(CircumferenceOf(Circle($)))].
Find z in the figure.,[Find(z)].
Find m \angle B.,[Find(MeasureOf(Angle(B)))].
AD and CG are diameters of \odot B. Find m \widehat GCF.,"[IsDiameterOf(Line(A,D),Circle(B))], [IsDiameterOf(Line(C,G),Circle(B))]. [Find(MeasureOf(Arc(G,C,F)))]."
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find m \angle 6.,[Find(MeasureOf(Angle(6)))].
Find JM.,"[Find(LengthOf(Line(J,M)))]."
"In the figure, \triangle ABC is isosceles, \triangle DCE is equilateral, and \triangle FCG is isosceles. Find the measure of the \angle 3 at vertex C.",", [Isosceles(Triangle(A,B,C))], [Equilateral(Triangle(D,C,E))] and [Isosceles(Triangle(F,C,G))]. [Find(MeasureOf(Angle(3)))], [Equals(Angle(3),Angle(C))]."
"In the figure, m \angle 1 = 53. Find the measure of \angle 6.",", [Equals(MeasureOf(Angle(1)),53)] [Find(MeasureOf(Angle(6)))]."
Find m \angle M.,[Find(MeasureOf(Angle(M)))].
Find h in the triangle.,[Find(h)] in [Triangle($)].
Find x.,[Find(x)].
"In rhombus ABCD, AB = 2x+3 and BC = 5x. Find m \angle BCD if m \angle ABC = 83.2.","In [Rhombus(A,B,C,D)], [Equals(LengthOf(Line(A,B)),2x+3)] and [Equals(LengthOf(Line(B,C)),5x)] [Find(MeasureOf(Angle(B,C,D)))] if [Equals(MeasureOf(Angle(A,B,C)),83.2)]."
Find the measure of \angle R.,[Find(MeasureOf(Angle(R)))].
\triangle KLN and \triangle LMN are isosceles and m \angle JKN = 130. Find the measure of \angle M.,"[Isosceles(Triangle(K,L,N))], [Isosceles(Triangle(L,M,N))] and [Equals(MeasureOf(Angle(J,K,N)),130)] [Find(MeasureOf(Angle(M)))]."
Find m \angle DGE.,"[Find(MeasureOf(Angle(D,G,E)))]."
"If QR = 2, XW = 12, QW = 15, and ST = 5, find WV.","If [Equals(LengthOf(Line(Q,R)),2)] [Equals(LengthOf(Line(X,W)),12)] [Equals(LengthOf(Line(Q,W)),15)] and [Equals(LengthOf(Line(S,T)),5)] [Find(LengthOf(Line(W,V)))]."
"In \odot A, m \angle EAD = 42. Find m \widehat CBE.","In [Circle(A)], [Equals(MeasureOf(Angle(E,A,D)),42)] [Find(MeasureOf(Arc(C,B,E)))]."
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
"In the figure, \triangle ABC is isosceles, \triangle DCE is equilateral, and \triangle FCG is isosceles. Find the measure of the \angle 2 at vertex C.",", [Isosceles(Triangle(A,B,C))], [Equilateral(Triangle(D,C,E))] and [Isosceles(Triangle(F,C,G))]. [Find(MeasureOf(Angle(2)))], [Equals(Angle(2),Angle(C))]."
Find x.,[Find(x)].
Use parallelogram ABCD to find the measure of m \angle ADC.,"Use [Parallelogram(A,B,C,D)] to [Find(MeasureOf(Angle(A,D,C)))]."
QRST is an isosceles trapezoid with median XY. Find TS if QR = 22 and XY = 15.,"[Isosceles(Quadrilateral(Q,R,S,T))] [Trapezoid($)], [IsMedianOf(Line(X,Y),Trapezoid($))]. [Find(LengthOf(Line(T,S)))] if [Equals(LengthOf(Line(Q,R)),22)] and [Equals(LengthOf(Line(X,Y)),15)]."
"In the figure, m \angle 1 = 94. Find the measure of \angle 3.",", [Equals(MeasureOf(Angle(1)),94)] [Find(MeasureOf(Angle(3)))]."
Quadrilateral WXYZ is inscribed in \odot V. Find m \angle Y.,"[InscribedIn(Quadrilateral(W,X,Y,Z),Circle(V))]. [Find(MeasureOf(Angle(Y)))]."
Find the measure of \angle 1 if AB \perp BC.,"[Find(MeasureOf(Angle(1)))] if [Perpendicular(Line(A,B),Line(B,C))]."
Rhombus WXYZ has an area of 100 square meters. Find WY if XZ = 10 meters.,"[Equals(AreaOf(Rhombus(W,X,Y,Z)),100)] [Find(LengthOf(Line(W,Y)))] if [Equals(LengthOf(Line(X,Z)),10)]."
"In the figure at the right, which cannot be true if m \parallel l and m \angle 1 = 73?",", which cannot be true if [Parallel(Line(m),Line(l))] and [Equals(MeasureOf(Angle(1)),73)]?"
Find the area of the shaded region. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth.
Solve for x in parallelogram RSTU.,"[Find(x)] in [Parallelogram(R,S,T,U)]."
Find BC.,"[Find(LengthOf(Line(B,C)))]."
"GRIDINIn the figure, the radius of circle A is twice the radius of circle B and four times the radius of circle C. If the sum of the circumferences of the three circles is 42\pi, find the measure of AC.",", [Equals(RadiusOf(Circle(A)),Mul(RadiusOf(Circle(B)),2))], [Equals(RadiusOf(Circle(A)),Mul(RadiusOf(Circle(C)),4))]. If [Equals(SumOf(CircumferenceOf(Circle($1)),CircumferenceOf(Circle($2)),CircumferenceOf(Circle($3))),42\pi)] [Find(LengthOf(Line(A,C)))]."
J is the incenter of \angle ABC. Find m \angle JAC.,"[IsIncenterOf(Point(J),Angle(A,B,C))]. [Find(MeasureOf(Angle(J,A,C)))]."
Find m \widehat TU.,"[Find(MeasureOf(Arc(T,U)))]."
Find WX.,"[Find(LengthOf(Line(W,X)))]."
Find m \widehat SU.,"[Find(MeasureOf(Arc(S,U)))]."
Find x.,[Find(x)].
Find x to the nearest tenth.,[Find(x)] to nearest tenth.
"In the figure, m \angle 1 = 53. Find the measure of \angle 5.",", [Equals(MeasureOf(Angle(1)),53)] [Find(MeasureOf(Angle(5)))]."
Find x. Round side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
Find m \angle T.,[Find(MeasureOf(Angle(T)))].
"\overrightarrow BA and \overrightarrow BC are opposite rays and \overrightarrow BD bisects \angle ABF. If m \angle ABF = 3x-8 and m \angle ABD = x+14, find m \angle ABD.","[Line(B,A)], [Line(B,C)], [PointLiesOnLine(B,Line(A,C))] and [BisectsAngle(Line(B,D),Angle(A,B,F))]. If [Equals(MeasureOf(Angle(A,B,F)),3x-8)] and [Equals(MeasureOf(Angle(A,B,D)),x+14)] [Find(MeasureOf(Angle(A,B,D)))]."
Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.,"[Find(x)] to nearest tenth. [Tangent(Line($),Circle($))]."
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
"In the figure, m \angle 3 = 43. Find the measure of \angle 10.",", [Equals(MeasureOf(Angle(3)),43)] [Find(MeasureOf(Angle(10)))]."
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
Find m \angle 3.,[Find(MeasureOf(Angle(3)))].
Find BE.,"[Find(LengthOf(Line(B,E)))]."
Find the area of the rhombus.,[Find(AreaOf(Rhombus($)))].
Find the area of the parallelogram.,[Find(AreaOf(Parallelogram($)))].
Find x.,[Find(x)].
"If \frac{IJ}{XJ} = \frac{HJ}{YJ}, m \angle WXJ = 130, and m \angle WZG = 20, find m \angle JIH.","If [Equals(RatioOf(Line(I,J),Line(X,J)),RatioOf(Line(H,J),Line(Y,J)))], [Equals(MeasureOf(Angle(W,X,J)),130)] and [Equals(MeasureOf(Angle(W,Z,G)),20)] [Find(MeasureOf(Angle(J,I,H)))]."
Find y.,[Find(y)].
Find x. Round to the nearest hundredth.,[Find(x)]. Round to nearest hundredth.
Find the measure of \angle T.,[Find(MeasureOf(Angle(T)))].
m \angle B = 76. The measure of \angle A is half the measure of \angle B. What is m \angle C?,"[Equals(MeasureOf(Angle(B)),76)] [Equals(MeasureOf(Angle(A)),HalfOf(MeasureOf(Angle(B))))]. [Find(MeasureOf(Angle(C)))]?"
"In the figure, FJ \cong FH and GF \cong GH. If m \angle JFH = 34, find m \angle J.",", [Equals(LengthOf(Line(F,J)),Line(F,H))] and [Equals(LengthOf(Line(G,F)),Line(G,H))]. If [Equals(MeasureOf(Angle(J,F,H)),34)] [Find(MeasureOf(Angle(J)))]."
Find x.,[Find(x)].
Find m \angle TUV.,"[Find(MeasureOf(Angle(T,U,V)))]."
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find the measure of \angle 3.,[Find(MeasureOf(Angle(3)))].
"Find the perimeter of \triangle CPD if the perimeter of \triangle BPA is 12, BM = \sqrt{13}, and CN = 3\sqrt{13}.","[Find(PerimeterOf(Triangle(C,P,D)))] if [Equals(PerimeterOf(Triangle(B,P,A)),12)] [Equals(LengthOf(Line(B,M)),\sqrt{13})] and [Equals(LengthOf(Line(C,N)),3\sqrt{13})]."
"In \triangle ACE, P is the centroid. PF = 6 and AD = 15. Find AP."," [Triangle(A,C,E)], [IsCentroidOf(Point(P),Triangle(A,C,E))]. [Equals(LengthOf(Line(P,F)),6)] and [Equals(LengthOf(Line(A,D)),15)] [Find(LengthOf(Line(A,P)))]."
Find the measure of \angle S.,[Find(MeasureOf(Angle(S)))].
Find the area of the shaded sector. Round to the nearest tenth.,[Find(AreaOf(Shaded(Sector($))))]. Round to nearest tenth.
Find m \angle X.,[Find(MeasureOf(Angle(X)))].
Find y in the figure.,[Find(y)].
If CN = 8. Find DN.,"If [Equals(LengthOf(Line(C,N)),8)] [Find(LengthOf(Line(D,N)))]."
Find y.,[Find(y)].
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find the measure of AC.,"[Find(LengthOf(Line(A,C)))]."
Find x to the nearest tenth.,[Find(x)] to nearest tenth.
"If XM = 4, XN = 6, and NZ = 9, find XY.","If [Equals(LengthOf(Line(X,M)),4)] [Equals(LengthOf(Line(X,N)),6)] and [Equals(LengthOf(Line(N,Z)),9)] [Find(LengthOf(Line(X,Y)))]."
m \widehat GH = 78. Find m \angle 2.,"[Equals(MeasureOf(Arc(G,H)),78)] [Find(MeasureOf(Angle(2)))]."
"Find the exact value of DE, given AD = 12 and BD = 4.","[Find(LengthOf(Line(D,E)))], [Equals(LengthOf(Line(A,D)),12)] and [Equals(LengthOf(Line(B,D)),4)]."
Find the scale factor from W to W'.,"[Find(ScaleFactorOf(Shape(W),Shape(W')))]."
Find z.,[Find(z)].
"In the figure, a \parallel b, c \parallel d, and m \angle 4 = 57. Find the measure of \angle 1.",", [Parallel(Line(a),Line(b))], [Parallel(Line(c),Line(d))] and [Equals(MeasureOf(Angle(4)),57)] [Find(MeasureOf(Angle(1)))]."
Find m \angle P.,[Find(MeasureOf(Angle(P)))].
"If \angle RST is a right angle, SU \perp RT, UV \perp ST, and m \angle RTS = 47, find m \angle RSU.","If [RightAngle(Angle(R,S,T))], [Perpendicular(Line(S,U),Line(R,T))], [Perpendicular(Line(U,V),Line(S,T))] and [Equals(MeasureOf(Angle(R,T,S)),47)] [Find(MeasureOf(Angle(R,S,U)))]."
Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. Round to nearest tenth if necessary. [Tangent(Line($),Circle($))]."
"In \triangle JKL, PT = 2. Find KP.","In [Triangle(J,K,L)], [Equals(LengthOf(Line(P,T)),2)] [Find(LengthOf(Line(K,P)))]."
Find m \angle SRT.,"[Find(MeasureOf(Angle(S,R,T)))]."
"ABCD is a rectangle. If AC = 9x-1 and AF = 2x+7, find AF."," [Rectangle(A,B,C,D)]. If [Equals(LengthOf(Line(A,C)),9x-1)] and [Equals(LengthOf(Line(A,F)),2x+7)] [Find(LengthOf(Line(A,F)))]."
"If PR \parallel KL, KN = 9, LN = 16, and PM = 2KP, find ML.","If [Parallel(Line(P,R),Line(K,L))], [Equals(LengthOf(Line(K,N)),9)] [Equals(LengthOf(Line(L,N)),16)] and [Equals(LengthOf(Line(P,M)),Mul(Line(K,P),2))], [Find(LengthOf(Line(M,L)))]."
"If TR = 8, LR = 3, and RW = 6, find WS.","If [Equals(LengthOf(Line(T,R)),8)] [Equals(LengthOf(Line(L,R)),3)] and [Equals(LengthOf(Line(R,W)),6)] [Find(LengthOf(Line(W,S)))]."
Find x.,[Find(x)].
The segment is tangent to the circle. Find x.,"[Tangent(Line($),Circle($))] to [Circle($)]. [Find(x)]."
Find the value of x.,[Find(x)].
Each triangle in the figure is a 30-60-90 triangle. Find x.,"[Equals(Triangle($),Triangle($1,$2,$3))], [Equals(MeasureOf(Angle($1)),30)], [Equals(MeasureOf(Angle($2)),60)], [Equals(MeasureOf(Angle($3)),90)]. [Find(x)]."
Find x.,[Find(x)].
Find the measure of \angle 2 if m \angle DGF = 53 and m \angle AGC = 40.,"[Find(MeasureOf(Angle(2)))] if [Equals(MeasureOf(Angle(D,G,F)),53)] and [Equals(MeasureOf(Angle(A,G,C)),40)]."
Find x.,[Find(x)].
Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. [Regular(Polygon($))]. Round to nearest tenth.
Find m \angle S.,[Find(MeasureOf(Angle(S)))].
find \tan A.,[Find(TanOf(Angle(A)))].
The segment is tangent to the circle. Find x.,"[Tangent(Line($),Circle($))] to [Circle($)]. [Find(x)]."
Find XZ.,"[Find(LengthOf(Line(X,Z)))]."
find \cos R.,[Find(CosOf(Angle(R)))].
Find y. Round to the nearest tenth.,[Find(y)]. Round to nearest tenth.
Find \angle 2.,[Find(MeasureOf(Angle(2)))].
Find y in the figure.,[Find(y)].
Each pair of polygons is similar. Find BC.,"[Similar(Polygon($1),Polygon($2))]. [Find(LengthOf(Line(B,C)))]."
Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. Round to nearest tenth if necessary. [Tangent(Line($),Circle($))]."
"Circle A has diameters DF and PG. If AG = 12, find LA.","[IsDiameterOf(Line(D,F),Circle(A))], [IsDiameterOf(Line(P,G),Circle(A))]. If [Equals(LengthOf(Line(A,G)),12)] [Find(LengthOf(Line(L,A)))]."
"The diagonals of rhombus FGHJ intersect at K. If m \angle FJH = 82, find m \angle KHJ.","[Rhombus(F,G,H,J)]. [IsDiagonalOf(Line(F,H),Rhombus(F,G,H,J))], [IsDiagonalOf(Line(G,J),Rhombus(F,G,H,J))]. [IntersectAt(Line(F,H),Line(G,J),Point(K))]. If [Equals(MeasureOf(Angle(F,J,H)),82)] [Find(MeasureOf(Angle(K,H,J)))]."
"Find the perimeter of \triangle DEF, if \triangle DEF \sim \triangle ACB.","[Find(PerimeterOf(Triangle(D,E,F)))], if [Similar(Triangle(D,E,F),Triangle(A,C,B))]."
"Quadrilateral ABCD is a rhombus. If m \angle DPC = 3x-15, find x."," [Rhombus(A,B,C,D)]. If [Equals(MeasureOf(Angle(D,P,C)),3x-15)] [Find(x)]."
Find x.,[Find(x)].
"a = 14, b = 48, and c = 50, find \cos B.","[Equals(a,14)] [Equals(b,48)] and [Equals(c,50)] [Find(CosOf(Angle(B)))]."
Find the variable of x to the nearest tenth.,[Find(x)] to nearest tenth.
Find x.,[Find(x)].
\odot C \cong \odot D. Find x.,"[Congruent(Circle(C),Circle(D))]. [Find(x)]."
"a = 14, b = 48, and c = 50, find \tan A.","[Equals(a,14)] [Equals(b,48)] and [Equals(c,50)] [Find(TanOf(Angle(A)))]."
Which of the following statements about the figure is true?,Which of following statements about [Shape($)] is true?
"In \odot Z, \angle WZX \cong \angle XZY, m \angle VZU = 4x, m \angle UZY = 2x+24, and VY and WU are diameters. Find m \widehat UY.","In [Circle(Z)], [Equals(Angle(W,Z,X),Angle(X,Z,Y))], [Equals(MeasureOf(Angle(V,Z,U)),4x)] [Equals(MeasureOf(Angle(U,Z,Y)),2x+24)] and [IsDiameterOf(Line(V,Y),Circle($))], [IsDiameterOf(Line(W,U),Circle($))]. [Find(MeasureOf(Arc(U,Y)))]."
Find the measure of \angle 6 if m \angle 4 = m \angle 5.,"[Find(MeasureOf(Angle(6)))] if [Equals(MeasureOf(Angle(4)),MeasureOf(Angle(5)))]."
Find m \angle B.,[Find(MeasureOf(Angle(B)))].
Find DC if DG and JM are altitudes and \triangle KJL \sim \triangle EDC.,"[Find(LengthOf(Line(D,C)))] if [IsAltitudeOf(Line(D,G),Shape($))], [IsAltitudeOf(Line(J,M),Shape($))] and [Similar(Triangle(K,J,L),Triangle(E,D,C))]."
Find m \angle A.,[Find(MeasureOf(Angle(A)))].
Find EC.,"[Find(LengthOf(Line(E,C)))]."
Use the Pythagorean Theorem to find the length of the hypotenuse of the right triangle.,[UseTheorem(Pythagorean_Theorem)] to [Find(LengthOf(HypotenuseOf(Right(Triangle($)))))].
The height of a triangle is 5 centimeters more than its base. The area of the triangle is 52 square centimeters. Find the base.,"[Equals(HeightOf(Triangle($)),Add(BaseOf(Polygon($)),5))]. [Equals(AreaOf(Triangle($)),52)] [Find(BaseOf(Polygon($)))]."
Find the area of the quadrilateral.,[Find(AreaOf(Quadrilateral($)))].
Find y.,[Find(y)].
Find RT.,"[Find(LengthOf(Line(R,T)))]."
"In \odot F, find m \widehat ADB.","In [Circle(F)], [Find(MeasureOf(Arc(A,D,B)))]."
Find y.,[Find(y)].
Find x.,[Find(x)].
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find the area of the figure.,[Find(AreaOf(Shape($)))].
Find the measure of \angle A. Round to the nearest degree.,[Find(MeasureOf(Angle(A)))]. Round to nearest degree.
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find the measure of \angle 3 in the figure.,[Find(MeasureOf(Angle(3)))].
"In \odot F, find m \widehat AED.","In [Circle(F)], [Find(MeasureOf(Arc(A,E,D)))]."
Find x.,[Find(x)].
Find x.,[Find(x)].
Find x.,[Find(x)].
Each pair of polygons is similar. Find y.,"[Similar(Polygon($1),Polygon($2))]. [Find(y)]."
Find the measure of \angle 2 if m \angle 4 = m \angle 5.,"[Find(MeasureOf(Angle(2)))] if [Equals(MeasureOf(Angle(4)),MeasureOf(Angle(5)))]."
The segment is tangent to the circle. Find x. Round to the nearest tenth.,"[Tangent(Line($),Circle($))] to [Circle($)]. [Find(x)]. Round to nearest tenth."
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
Find the value of x.,[Find(x)].
"JH, JP, and PH are midsegments of \triangle KLM. Find x.","[IsMidsegmentOf(Line(J,H),Triangle(K,L,M))], [IsMidsegmentOf(Line(J,P),Triangle(K,L,M))], [IsMidsegmentOf(Line(P,H),Triangle(K,L,M))],. [Find(x)]."
"If RT = 16, QP = 24, and ST = 9, find PS.","If [Equals(LengthOf(Line(R,T)),16)] [Equals(LengthOf(Line(Q,P)),24)] and [Equals(LengthOf(Line(S,T)),9)] [Find(LengthOf(Line(P,S)))]."
"Circle O has a radius of 10, AB = 10 and m \overrightarrow AB = 60. Find m \widehat AX.","[Equals(RadiusOf(Circle(O)),10)] [Equals(LengthOf(Line(A,B)),10)] and [Equals(LengthOf(Line(A,B)),60)] [Find(MeasureOf(Arc(A,X)))]."
"For trapezoid QRST, M and P are midpoints of the legs. If TS = 2x, PM = 20, and QR = 6x, find x.","[Trapezoid(Q,R,S,T)], [IsMidpointOf(Point(M),LegOf(Trapezoid(Q,R,S,T)))], [IsMidpointOf(Point(P),LegOf(Trapezoid(Q,R,S,T)))],. If [Equals(LengthOf(Line(T,S)),2x)] [Equals(LengthOf(Line(P,M)),20)] and [Equals(LengthOf(Line(Q,R)),6x)] [Find(x)]."
"In \odot C, m \angle HCG = 2x and m \angle HCD = 6x+28, find m \widehat EF.","In [Circle(C)], [Equals(MeasureOf(Angle(H,C,G)),2x)] and [Equals(MeasureOf(Angle(H,C,D)),6x+28)] [Find(MeasureOf(Arc(E,F)))]."
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Find the circumference of \odot S. Round to the nearest hundredth.,[Find(CircumferenceOf(Circle(S)))]. Round to nearest hundredth.
Find the measure of \angle 2.,[Find(MeasureOf(Angle(2)))].
"JKMN is a rectangle. If NQ = 2x+3 and QK = 5x-9, find JQ."," [Rectangle(J,K,M,N)]. If [Equals(LengthOf(Line(N,Q)),2x+3)] and [Equals(LengthOf(Line(Q,K)),5x-9)] [Find(LengthOf(Line(J,Q)))]."
Find AB.,"[Find(LengthOf(Line(A,B)))]."
Find the measure of x.,[Find(MeasureOf(x))].
Each pair of polygons is similar. Find x.,"[Similar(Polygon($1),Polygon($2))]. [Find(x)]."
Find DE.,"[Find(LengthOf(Line(D,E)))]."
Find x.,[Find(x)].
"If QRST is a parallelogram, find x.","If [Parallelogram(Q,R,S,T)], [Find(x)]."
Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. [Regular(Polygon($))]. Round to nearest tenth.
Find y.,[Find(y)].
"Chords AC and DF are equidistant from the center. If the radius of \odot G is 26, find DE.","[IsChordOf(Line(A,C),Circle($))], [IsChordOf(Line(D,F),Circle($))]. [Line(A,C)] and [Line(D,F)] are equidistant from center. If [Equals(RadiusOf(Circle(G)),26)] [Find(LengthOf(Line(D,E)))]."
"Find UB if \triangle RST \sim \triangle UVW, TA and WB are medians, TA = 8, RA = 3, WB = 3x-6, and UB = x+2.","[Find(LengthOf(Line(U,B)))] if [Similar(Triangle(R,S,T),Triangle(U,V,W))], [IsMedianOf(Line(T,A),Shape($))], [IsMedianOf(Line(W,B),Shape($))], [Equals(LengthOf(Line(T,A)),8)] [Equals(LengthOf(Line(R,A)),3)] [Equals(LengthOf(Line(W,B)),3x-6)] and [Equals(LengthOf(Line(U,B)),x+2)]."
Find x.,[Find(x)].
Find the area of the shaded region. Assume the inscribed polygon is regular.,[Find(AreaOf(Shaded(Shape($))))]. Assume inscribed [Regular(Polygon($))].
"For trapezoid TRSV, M and N are midpoints of the legs. If VS = 21 and TR = 44, find MN.","[Trapezoid(T,R,S,V)], [IsMidpointOf(Point(M),LegOf(Trapezoid(T,R,S,V)))], [IsMidpointOf(Point(N),LegOf(Trapezoid(T,R,S,V)))],. If [Equals(LengthOf(Line(V,S)),21)] and [Equals(LengthOf(Line(T,R)),44)] [Find(LengthOf(Line(M,N)))]."
Find \tan B.,[Find(TanOf(Angle(B)))].
"In \odot G, m \angle AGB = 30 and CG \perp GD. Find m \widehat AB.","In [Circle(G)], [Equals(MeasureOf(Angle(A,G,B)),30)] and [Perpendicular(Line(C,G),Line(G,D))]. [Find(MeasureOf(Arc(A,B)))]."
Find UZ.,"[Find(LengthOf(Line(U,Z)))]."
Find the perimeter of the polygon for the given information.,[Find(PerimeterOf(Polygon($)))] for.
Find the measure of \angle 1.,[Find(MeasureOf(Angle(1)))].
Express the ratio of \cos M as a decimal to the nearest hundredth.,[Find(RatioOf(CosOf(Angle(M))))] to nearest hundredth.
Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. Round to nearest tenth if necessary. [Tangent(Line($),Circle($))]."
Find y in the figure.,[Find(y)].
"In the figure, m \angle 4 = 104, m \angle 14 = 118. Find the measure of \angle 9.",", [Equals(MeasureOf(Angle(4)),104)] [Equals(MeasureOf(Angle(14)),118)] [Find(MeasureOf(Angle(9)))]."
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
"If m \angle S = 3x and m \angle V = x+16, find m \angle S.","If [Equals(MeasureOf(Angle(S)),3x)] and [Equals(MeasureOf(Angle(V)),x+16)] [Find(MeasureOf(Angle(S)))]."
Find m \angle 6.,[Find(MeasureOf(Angle(6)))].
find \tan R.,[Find(TanOf(Angle(R)))].
"If quadrilateral ABCD is a kite, what is m \angle C?","If  [Kite(A,B,C,D)], [Find(MeasureOf(Angle(C)))]?"
Find AB.,"[Find(LengthOf(Line(A,B)))]."
Each pair of polygons is similar. Find x.,"[Similar(Polygon($1),Polygon($2))]. [Find(x)]."
Find x.,[Find(x)].
Find the area of the shaded region. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth.
Find the area of the kite.,[Find(AreaOf(Kite($)))].
Find x.,[Find(x)].
"In the figure, CP is an altitude, CQ is the angle bisector of \angle ACB, and R is the midpoint of AB. Find x if m \angle APC = 72+x.",", [IsAltitudeOf(Line(C,P),Shape($))], [BisectsAngle(Line(C,Q),Angle(A,C,B))] and [IsMidpointOf(Point(R),Line(A,B))]. [Find(x)] if [Equals(MeasureOf(Angle(A,P,C)),72+x)]."
Find y.,[Find(y)].
Find AC if \triangle ABC is an isosceles triangle with AB \cong BC.,"[Find(LengthOf(Line(A,C)))] if [Isosceles(Triangle(A,B,C))] with [Equals(LengthOf(Line(A,B)),Line(B,C))]."
Find y.,[Find(y)].
Find y in the figure.,[Find(y)].
Find m \angle B.,[Find(MeasureOf(Angle(B)))].
Quadrilateral ABCD is a rectangle. m \angle 2 = 40. Find m \angle 5.," [Rectangle(A,B,C,D)]. [Equals(MeasureOf(Angle(2)),40)] [Find(MeasureOf(Angle(5)))]."
"Find the perimeter of the given triangle \triangle DEF, if \triangle ABC \sim \triangle DEF, AB = 5, BC = 6, AC = 7, and DE = 3.","[Find(PerimeterOf(Triangle(D,E,F)))], if [Similar(Triangle(A,B,C),Triangle(D,E,F))], [Equals(LengthOf(Line(A,B)),5)] [Equals(LengthOf(Line(B,C)),6)] [Equals(LengthOf(Line(A,C)),7)] and [Equals(LengthOf(Line(D,E)),3)]."
Find x.,[Find(x)].
Find the value of the variable y in the figure.,[Find(y)].
"Find the perimeter of the polygon for the given information. CF = 6(3-x), DB = 12y-4.","[Find(PerimeterOf(Polygon($)))] for. [Equals(LengthOf(Line(C,F)),6(3-x))] [Equals(LengthOf(Line(D,B)),12y-4)]."
Find x.,[Find(x)].
Find x.,[Find(x)].
Find the measure of \angle 2 in the figure.,[Find(MeasureOf(Angle(2)))].
The square is circumscribed to the circle. Find the exact circumference of the circle.,"[CircumscribedTo(Square($),Circle($))]. [Find(CircumferenceOf(Circle($)))]."
Find x.,[Find(x)].
Find x. (Hint: Draw an auxiliary line).,[Find(x)]. (Hint: Draw auxiliary line).
Express the ratio of \sin B as a decimal to the nearest hundredth.,[Find(RatioOf(SinOf(Angle(B))))] to nearest hundredth.
"ABCD is a rhombus. If PB = 12, AB = 15, and m \angle ABD = 24. Find m \angle ACB."," [Rhombus(A,B,C,D)]. If [Equals(LengthOf(Line(P,B)),12)] [Equals(LengthOf(Line(A,B)),15)] and [Equals(MeasureOf(Angle(A,B,D)),24)] [Find(MeasureOf(Angle(A,C,B)))]."
Find h in the triangle.,[Find(h)] in [Triangle($)].
Find AE.,"[Find(LengthOf(Line(A,E)))]."
Express the ratio of \tan B as a decimal to the nearest hundredth.,[Find(RatioOf(TanOf(Angle(B))))] to nearest hundredth.
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find y so that BE and AD are perpendicular.,"[Find(y)] so [Perpendicular(Line(B,E),Line(A,D))]."
Use parallelogram MNPR to find m \angle MQR.,"Use [Parallelogram(M,N,P,R)] to [Find(MeasureOf(Angle(M,Q,R)))]."
Find x.,[Find(x)].
Find z.,[Find(z)].
Find x.,[Find(x)].
Find x.,[Find(x)].
What is the measure of \angle KLM.,"[Find(MeasureOf(Angle(K,L,M)))]."
Find x.,[Find(x)].
Find the length of XW.,"[Find(LengthOf(Line(X,W)))]."
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
"Polygon ABCD \sim polygon AEFG, m \angle AGF = 108, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26. Find the perimeter of trapezoid AEFG.","[Similar(Quadrilateral(A,B,C,D),Quadrilateral(A,E,F,G))], [Equals(MeasureOf(Angle(A,G,F)),108)] [Equals(LengthOf(Line(G,F)),14)] [Equals(LengthOf(Line(A,D)),12)] [Equals(LengthOf(Line(D,G)),4.5)] [Equals(LengthOf(Line(E,F)),8)] and [Equals(LengthOf(Line(A,B)),26)] [Find(PerimeterOf(Trapezoid(A,E,F,G)))]."
"Quadrilateral WXZY is a rhombus. If m \angle XZY = 56, find m \angle YWZ."," [Rhombus(W,X,Z,Y)]. If [Equals(MeasureOf(Angle(X,Z,Y)),56)] [Find(MeasureOf(Angle(Y,W,Z)))]."
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find y.,[Find(y)].
Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. Round to nearest tenth if necessary. [Tangent(Line($),Circle($))]."
"The diameter of \odot S is 30 units, the diameter of \odot R is 20 units, and DS = 9 units. Find CD.","[Equals(DiameterOf(Circle(S)),30)] [Equals(DiameterOf(Circle(R)),20)] and [Equals(LengthOf(Line(D,S)),9)] [Find(LengthOf(Line(C,D)))]."
Find the scale factor from W to W'.,"[Find(ScaleFactorOf(Shape(W),Shape(W')))]."
"If x = 7\sqrt{3}, find y.","If [Equals(x,7\sqrt{3})] [Find(y)]."
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
"In \triangle PQR, ST \parallel RQ. If PT = 7.5, TQ = 3, and SR = 2.5, find PS.","In [Triangle(P,Q,R)], [Parallel(Line(S,T),Line(R,Q))]. If [Equals(LengthOf(Line(P,T)),7.5)] [Equals(LengthOf(Line(T,Q)),3)] and [Equals(LengthOf(Line(S,R)),2.5)] [Find(LengthOf(Line(P,S)))]."
"UJ = 9, VJ = 3, and ZT = 18. Find JT.","[Equals(LengthOf(Line(U,J)),9)] [Equals(LengthOf(Line(V,J)),3)] and [Equals(LengthOf(Line(Z,T)),18)] [Find(LengthOf(Line(J,T)))]."
Find the angle measure of \angle 3.,[Find(MeasureOf(Angle(3)))].
Find x.,[Find(x)].
"The diameters of \odot A, \odot B, and \odot C are 8 inches, 18 inches, and 11 inches, respectively. Find FB.","[Equals(DiameterOf(Circle(A)),8)] [Equals(DiameterOf(Circle(B)),18)] [Equals(DiameterOf(Circle(C)),11)] [Find(LengthOf(Line(F,B)))]."
"If WP is a median and an angle bisector, AP = 3y+11, PH = 7y-5, m \angle HWP = x+12, m \angle PAW = 3x-2, and m \angle HWA = 4x-16, find y.","If [IsMedianOf(Line(W,P),Shape($))], [BisectsAngle(Line(W,P),Angle($))], [Equals(LengthOf(Line(A,P)),3y+11)] [Equals(LengthOf(Line(P,H)),7y-5)] [Equals(MeasureOf(Angle(H,W,P)),x+12)] [Equals(MeasureOf(Angle(P,A,W)),3x-2)] and [Equals(MeasureOf(Angle(H,W,A)),4x-16)] [Find(y)]."
"In the figure, m \angle 8 = 96 and m \angle 12 = 42. Find the measure of \angle 9.",", [Equals(MeasureOf(Angle(8)),96)] and [Equals(MeasureOf(Angle(12)),42)] [Find(MeasureOf(Angle(9)))]."
Find the area of the triangle.,[Find(AreaOf(Triangle($)))].
Find x in parallelogram ABCD.,"[Find(x)] in [Parallelogram(A,B,C,D)]."
"ABCD is a rhombus. If PB = 12, AB = 15, and m \angle ABD = 24. Find AP."," [Rhombus(A,B,C,D)]. If [Equals(LengthOf(Line(P,B)),12)] [Equals(LengthOf(Line(A,B)),15)] and [Equals(MeasureOf(Angle(A,B,D)),24)] [Find(LengthOf(Line(A,P)))]."
"If PQ \cong UQ, PR \cong RT and m \angle PQU = 40, find m \angle R.","If [Equals(LengthOf(Line(P,Q)),Line(U,Q))], [Equals(LengthOf(Line(P,R)),Line(R,T))] and [Equals(MeasureOf(Angle(P,Q,U)),40)] [Find(MeasureOf(Angle(R)))]."
"In \odot F, GK = 14 and m \widehat GHK = 142. Find m \widehat KM.","In [Circle(F)], [Equals(LengthOf(Line(G,K)),14)] and [Equals(MeasureOf(Arc(G,H,K)),142)] [Find(MeasureOf(Arc(K,M)))]."
Find x.,[Find(x)].
Each pair of polygons is similar. Find CD.,"[Similar(Polygon($1),Polygon($2))]. [Find(LengthOf(Line(C,D)))]."
Find x. A = 104 ft^2.,"[Find(x)]. [Equals(AreaOf(Shape(A)),104)]."
"If ABCDE \sim PQRST, find the perimeter of ABCDE.","If [Similar(Pentagon(A,B,C,D,E),Pentagon(P,Q,R,S,T))], [Find(PerimeterOf(Pentagon(A,B,C,D,E)))]."
Find m \angle JKL.,"[Find(MeasureOf(Angle(J,K,L)))]."
Find the area of the shaded sector. Round to the nearest tenth.,[Find(AreaOf(Shaded(Sector($))))]. Round to nearest tenth.
Find y in the figure.,[Find(y)].
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
"If PQ \cong UQ and m \angle P = 32, find m \angle PUQ.","If [Equals(LengthOf(Line(P,Q)),Line(U,Q))] and [Equals(MeasureOf(Angle(P)),32)] [Find(MeasureOf(Angle(P,U,Q)))]."
"If PR \parallel WX, WX = 10, XY = 6, WY = 8, RY = 5, and PS = 3, find PQ.","If [Parallel(Line(P,R),Line(W,X))], [Equals(LengthOf(Line(W,X)),10)] [Equals(LengthOf(Line(X,Y)),6)] [Equals(LengthOf(Line(W,Y)),8)] [Equals(LengthOf(Line(R,Y)),5)] and [Equals(LengthOf(Line(P,S)),3)] [Find(LengthOf(Line(P,Q)))]."
Find x.,[Find(x)].
Find the measure of \angle C. Round to the nearest degree.,[Find(MeasureOf(Angle(C)))]. Round to nearest degree.
"In the figure, QR \parallel TS, QT \parallel RS, and m \angle 1 = 131. Find the measure of \angle 4.",", [Parallel(Line(Q,R),Line(T,S))], [Parallel(Line(Q,T),Line(R,S))] and [Equals(MeasureOf(Angle(1)),131)] [Find(MeasureOf(Angle(4)))]."
Find x.,[Find(x)].
"If CE = t-2. EB = t+1, CD = 2, and CA = 10, find t.","If [Equals(LengthOf(Line(C,E)),t-2)] [Equals(LengthOf(Line(E,B)),t+1)] [Equals(LengthOf(Line(C,D)),2)] and [Equals(LengthOf(Line(C,A)),10)] [Find(t)]."
Find m \angle ACD.,"[Find(MeasureOf(Angle(A,C,D)))]."
Find m \widehat RQS if m \widehat QTS = 238.,"[Find(MeasureOf(Arc(R,Q,S)))] if [Equals(MeasureOf(Arc(Q,T,S)),238)]."
Find x. Round the side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
Find x.,[Find(x)].
Use a Pythagorean Triple to find x.,[UseTheorem(Pythagorean_Triple)] to [Find(x)].
"In the figure, m \angle 3 = 43. Find the measure of \angle 2.",", [Equals(MeasureOf(Angle(3)),43)] [Find(MeasureOf(Angle(2)))]."
Use parallelogram WXYZ to find WZ.,"Use [Parallelogram(W,X,Y,Z)] to [Find(LengthOf(Line(W,Z)))]."
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
"Use rectangle LMNP, parallelogram LKMJ to solve the problem. If MK = 6x, KL = 3x+2y, and JN = 14-x, find y.","Use [Rectangle(L,M,N,P)], [Parallelogram(L,K,M,J)] to. If [Equals(LengthOf(Line(M,K)),6x)] [Equals(LengthOf(Line(K,L)),3x+2y)] and [Equals(LengthOf(Line(J,N)),14-x)] [Find(y)]."
Find m \angle 3.,[Find(MeasureOf(Angle(3)))].
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
"Quadrilateral RSTU is circumscribed about \odot J. If the preimeter is 18 units, find x.","[CircumscribedTo(Quadrilateral(R,S,T,U),Circle(J))]. If [Equals(PerimeterOf(Polygon($)),18)] [Find(x)]."
"Given figure ABCD, with AB \parallel DC, m \angle B = 60, m \angle D = 45, BC = 8 and AB = 24, find the perimeter.","[Quadrilateral(A,B,C,D)], with [Parallel(Line(A,B),Line(D,C))], [Equals(MeasureOf(Angle(B)),60)] [Equals(MeasureOf(Angle(D)),45)] [Equals(LengthOf(Line(B,C)),8)] and [Equals(LengthOf(Line(A,B)),24)] [Find(PerimeterOf(Polygon($)))]."
Find the circumference of the figure. Round to the nearest tenth.,[Find(CircumferenceOf(Shape($)))]. Round to nearest tenth.
Find x to the nearest hundredth.,[Find(x)] to nearest hundredth.
Find the area of \parallelogram EFGH.,"[Find(AreaOf(Parallelogram(E,F,G,H)))]."
Find the measure of \angle 8 if AB \perp BC.,"[Find(MeasureOf(Angle(8)))] if [Perpendicular(Line(A,B),Line(B,C))]."
"If SP = 4, PT = 6, and QR = 12, find SQ.","If [Equals(LengthOf(Line(S,P)),4)] [Equals(LengthOf(Line(P,T)),6)] and [Equals(LengthOf(Line(Q,R)),12)] [Find(LengthOf(Line(S,Q)))]."
Find x in the figure.,[Find(x)].
"Find CD if AB = 6, AF = 8, BC = x, CD = y, DE = 2y-3, and FE = x+\frac{10}{3}.","[Find(LengthOf(Line(C,D)))] if [Equals(LengthOf(Line(A,B)),6)] [Equals(LengthOf(Line(A,F)),8)] [Equals(LengthOf(Line(B,C)),x)] [Equals(LengthOf(Line(C,D)),y)] [Equals(LengthOf(Line(D,E)),2y-3)] and [Equals(LengthOf(Line(F,E)),x+\frac{10}{3})]."
Find m \angle PQS.,"[Find(MeasureOf(Angle(P,Q,S)))]."
"The sum of the circumference of circles H, J, K is 56\pi units. Find KJ.","[Equals(SumOf(CircumferenceOf(Circle(H)),Circle(J),Circle(K)),56\pi)] [Find(LengthOf(Line(K,J)))]."
Find m \angle 3.,[Find(MeasureOf(Angle(3)))].
Find AS.,"[Find(LengthOf(Line(A,S)))]."
Find the perimeter of the triangle. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Triangle($)))]. Round to nearest tenth if necessary.
Find the area of the shaded region. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth.
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
Find the value of x in the diagram.,[Find(x)].
Find x.,[Find(x)].
Find the area of the trapezoid.,[Find(AreaOf(Trapezoid($)))].
Use parallelogram ABCD to find m \angle BDC.,"Use [Parallelogram(A,B,C,D)] to [Find(MeasureOf(Angle(B,D,C)))]."
"The diameters of \odot A, \odot B, and \odot C are 10 inches, 20 inches, and 14 inches, respectively. Find BY.","[Equals(DiameterOf(Circle(A)),10)] [Equals(DiameterOf(Circle(B)),20)] [Equals(DiameterOf(Circle(C)),14)] [Find(LengthOf(Line(B,Y)))]."
Find x.,[Find(x)].
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Find x. Round the side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
"Find the perimeter of the figure. Round to the nearest hundredth, if necessary.","[Find(PerimeterOf(Shape($)))]. Round to nearest hundredth, if necessary."
Find m \angle JMK.,"[Find(MeasureOf(Angle(J,M,K)))]."
Find x.,[Find(x)].
"In \odot P, m \widehat EN = 66 and m \angle GPM = 89. Find m \angle GNM.","In [Circle(P)], [Equals(MeasureOf(Arc(E,N)),66)] and [Equals(MeasureOf(Angle(G,P,M)),89)] [Find(MeasureOf(Angle(G,N,M)))]."
Find x.,[Find(x)].
Find x. A = 177 cm^2.,"[Find(x)]. [Equals(AreaOf(Shape(A)),177)]."
Find z.,[Find(z)].
"If QRST is a parallelogram, find y.","If [Parallelogram(Q,R,S,T)], [Find(y)]."
Find the perimeter of the triangle. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Triangle($)))]. Round to nearest tenth if necessary.
Find m \angle B.,[Find(MeasureOf(Angle(B)))].
Find x.,[Find(x)].
Find x.,[Find(x)].
Find x. Round the angle measure to the nearest degree.,[Find(x)]. Round angle measure to nearest degree.
Find x.,[Find(x)].
Find y and so that the quadrilateral is a parallelogram.,[Find(y)] and so [Parallelogram($)]
"If ABCD is a kite, find AB.","If [Kite(A,B,C,D)], [Find(LengthOf(Line(A,B)))]."
Find y.,[Find(y)].
Find the value of the variable y in the figure.,[Find(y)].
Find m \angle RCL.,"[Find(MeasureOf(Angle(R,C,L)))]."
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find the area of the trapezoid.,[Find(AreaOf(Trapezoid($)))].
"The lengths of the bases of an isosceles trapezoid are shown below. If the perimeter is 74 meters, what is its area?","lengths of bases of [Isosceles(Trapezoid($))] are. If [Equals(PerimeterOf(Polygon($)),74)] [Find(AreaOf(Polygon($)))]?"
Find m \widehat RT.,"[Find(MeasureOf(Arc(R,T)))]."
Find m \widehat YC.,"[Find(MeasureOf(Arc(Y,C)))]."
Find y so that e \parallel f.,"[Find(y)] so [Parallel(Line(e),Line(f))]."
Find the measure of m \angle 3. Assume that segments that appear tangent are tangent.,"[Find(MeasureOf(Angle(3)))]. [Tangent(Line($),Circle($))]."
Find y. Round to the nearest tenth.,[Find(y)]. Round to nearest tenth.
Find AX if EX = 24 and DE = 7.,"[Find(LengthOf(Line(A,X)))] if [Equals(LengthOf(Line(E,X)),24)] and [Equals(LengthOf(Line(D,E)),7)]."
Find x.,[Find(x)].
Find the area of the shaded region. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth.
Find m \angle R.,[Find(MeasureOf(Angle(R)))].
"Quadrilateral WXYZ is a rectangle. If XW = 3, WZ = 4, and XZ = b, find YW."," [Rectangle(W,X,Y,Z)]. If [Equals(LengthOf(Line(X,W)),3)] [Equals(LengthOf(Line(W,Z)),4)] and [Equals(LengthOf(Line(X,Z)),b)] [Find(LengthOf(Line(Y,W)))]."
Find y in the given parallelogram.,[Find(y)] in [Parallelogram($)].
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find the area of the shaded region. Assume that the polygon is regular unless otherwise stated. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. [Regular(Polygon($))]. Round to nearest tenth.
"m \angle 9 = 2x-4, m \angle 10 = 2x+4. Find the measure of \angle 9.","[Equals(MeasureOf(Angle(9)),2x-4)] [Equals(MeasureOf(Angle(10)),2x+4)] [Find(MeasureOf(Angle(9)))]."
The segment is tangent to the circle. Find x.,"[Tangent(Line($),Circle($))] to [Circle($)]. [Find(x)]."
The radius of \odot P is 5 and PR = 3. Find QS.,"[Equals(RadiusOf(Circle(P)),5)] and [Equals(LengthOf(Line(P,R)),3)] [Find(LengthOf(Line(Q,S)))]."
Find the area of the trapezoid.,[Find(AreaOf(Trapezoid($)))].
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
H is the incenter of \triangle ABC. Find DH.,"[IsIncenterOf(Point(H),Triangle(A,B,C))]. [Find(LengthOf(Line(D,H)))]."
"ABCD is a rhombus. If PB = 12, AB = 15, and m \angle ABD = 24. Find CP."," [Rhombus(A,B,C,D)]. If [Equals(LengthOf(Line(P,B)),12)] [Equals(LengthOf(Line(A,B)),15)] and [Equals(MeasureOf(Angle(A,B,D)),24)] [Find(LengthOf(Line(C,P)))]."
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
"If m \angle 1 = 3x+40, m \angle 2 = 2(y-10), and m \angle 3 = 2x+70, find x.","If [Equals(MeasureOf(Angle(1)),3x+40)] [Equals(MeasureOf(Angle(2)),2(y-10))] and [Equals(MeasureOf(Angle(3)),2x+70)] [Find(x)]."
"A plane travels from Des Moines to Phoenix, on to Atlanta, and back to Des Moines, as shown below. Find the distance in miles from Atlanta to Des Moines if the total trip was 3482 miles.","A plane travels from Des Moines to Phoenix, on to Atlanta and back to Des Moines,. Find distance in from Atlanta to Des Moines if trip was 3482."
"parallelogram MNPQ with m \angle M = 10x and m \angle N = 20x, find \angle P.","[Parallelogram(M,N,P,Q)] with [Equals(MeasureOf(Angle(M)),10x)] and [Equals(MeasureOf(Angle(N)),20x)] [Find(MeasureOf(Angle(P)))]."
Find x. A = 153 in^2.,"[Find(x)]. [Equals(AreaOf(Shape(A)),153)]."
Find the area of the shaded sector. Round to the nearest tenth.,[Find(AreaOf(Shaded(Sector($))))]. Round to nearest tenth.
"Quadrilateral MNOP is a rectangle. If MO = 6x+14 and PN = 9x+5, find x."," [Rectangle(M,N,O,P)]. If [Equals(LengthOf(Line(M,O)),6x+14)] and [Equals(LengthOf(Line(P,N)),9x+5)] [Find(x)]."
Find \angle D of quadrilateral ABCD.,"[Find(MeasureOf(Angle(D)))] of [Quadrilateral(A,B,C,D)]."
"In the figure, m \angle 9 = 75. Find the measure of \angle 12.",", [Equals(MeasureOf(Angle(9)),75)] [Find(MeasureOf(Angle(12)))]."
Find m \widehat JK.,"[Find(MeasureOf(Arc(J,K)))]."
Refer to the triangle shown below. Find z to the nearest tenth.,[Triangle($)]. [Find(z)] to nearest tenth.
"If \angle RST is a right angle, SU \perp RT, UV \perp ST, and m \angle RTS = 47, find m \angle TUV.","If [RightAngle(Angle(R,S,T))], [Perpendicular(Line(S,U),Line(R,T))], [Perpendicular(Line(U,V),Line(S,T))] and [Equals(MeasureOf(Angle(R,T,S)),47)] [Find(MeasureOf(Angle(T,U,V)))]."
Find x so that m \parallel n.,"[Find(x)] so [Parallel(Line(m),Line(n))]."
"If AD = 24, find CN.","If [Equals(LengthOf(Line(A,D)),24)] [Find(LengthOf(Line(C,N)))]."
Find x.,[Find(x)].
Find m \angle U.,[Find(MeasureOf(Angle(U)))].
Find m \angle JLK.,"[Find(MeasureOf(Angle(J,L,K)))]."
Find the ratio of the area of \triangle ABC to the area of square BCDE.,"[Find(RatioOf(AreaOf(Triangle(A,B,C)),AreaOf(Square(B,C,D,E))))]."
"The diameters of \odot A, \odot B, and \odot C are 10, 30 and 10 units, respectively. Find BX if AZ \cong CW and CW = 2.","[Equals(DiameterOf(Circle(A)),10)] [Equals(DiameterOf(Circle(B)),30)] [Equals(DiameterOf(Circle(C)),10)] [Find(LengthOf(Line(B,X)))] if [Equals(LengthOf(Line(A,Z)),Line(C,W))] and [Equals(LengthOf(Line(C,W)),2)]."
Each pair of polygons is similar. Find CE.,"[Similar(Polygon($1),Polygon($2))]. [Find(LengthOf(Line(C,E)))]."
Express the ratio of \tan A as a decimal to the nearest hundredth.,[Find(RatioOf(TanOf(Angle(A))))] to nearest hundredth.
"If RT = 15, QP = 21, and PT = 8, find TS.","If [Equals(LengthOf(Line(R,T)),15)] [Equals(LengthOf(Line(Q,P)),21)] and [Equals(LengthOf(Line(P,T)),8)] [Find(LengthOf(Line(T,S)))]."
Find the variable of r to the nearest tenth. Assume that segments that appear to be tangent are tangent.,"[Find(r)] to nearest tenth. [Tangent(Line($),Circle($))]."
Find the area of the kite.,[Find(AreaOf(Kite($)))].
Find the measure of \angle 3 if m \angle DGF = 53 and m \angle AGC = 40.,"[Find(MeasureOf(Angle(3)))] if [Equals(MeasureOf(Angle(D,G,F)),53)] and [Equals(MeasureOf(Angle(A,G,C)),40)]."
Find y.,[Find(y)].
Find z.,[Find(z)].
What is the area of the shaded region if r = 4.,"[Find(AreaOf(Shaded(Shape($))))] if [Equals(r,4)]."
Find the measure of \angle B.,[Find(MeasureOf(Angle(B)))].
\triangle PQS \cong \triangle RQS. Find x.,"[Congruent(Triangle(P,Q,S),Triangle(R,Q,S))]. [Find(x)]."
What is the area of the triangle below? Round your answer to the nearest tenth if necessary.,[Find(AreaOf(Triangle($)))]? Round to nearest tenth if necessary.
"In \odot J, GH = 9 and KL = 4x+1. Find x.","In [Circle(J)], [Equals(LengthOf(Line(G,H)),9)] and [Equals(LengthOf(Line(K,L)),4x+1)] [Find(x)]."
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
Find x.,[Find(x)].
Find the value of x in the diagram.,[Find(x)].
Triangle CDE has an area of 336 square inches. Find CE.,"[Equals(AreaOf(Triangle(C,D,E)),336)] [Find(LengthOf(Line(C,E)))]."
Find y.,[Find(y)].
Find the area of the shaded region. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth.
Find x.,[Find(x)].
Find y.,[Find(y)].
What is the measure of an interior angle of a regular pentagon?,[Find(MeasureOf(Angle($)))] of [Regular(Pentagon($))]?
"If WP is a perpendicular bisector, m \angle WHA = 8q+17, m \angle HWP = 10+q, AP = 6r+4, and PH = 22+3r, find q.","If [IsPerpendicularBisectorOf(Line(W,P),Line($))], [Equals(MeasureOf(Angle(W,H,A)),8q+17)] [Equals(MeasureOf(Angle(H,W,P)),10+q)] [Equals(LengthOf(Line(A,P)),6r+4)] and [Equals(LengthOf(Line(P,H)),22+3r)] [Find(q)]."
"In \triangle ABC, BD is a median. If AD = 3x+5 and CD = 5x-1, find AC.","[Triangle(A,B,C)], [IsMedianOf(Line(B,D),Triangle(A,B,C))]. If [Equals(LengthOf(Line(A,D)),3x+5)] and [Equals(LengthOf(Line(C,D)),5x-1)] [Find(LengthOf(Line(A,C)))]."
Find y.,[Find(y)].
Refer to trapezoid CDFG with median HE. Let WX be the median of CDEH. Find WX.,"[Trapezoid(C,D,F,G)], [IsMedianOf(Line(H,E),Trapezoid(C,D,F,G))]. Let [IsMedianOf(Line(W,X),Quadrilateral(C,D,E,H))]. [Find(LengthOf(Line(W,X)))]."
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find the perimeter of the parallelogram.,[Find(PerimeterOf(Parallelogram($)))].
Point S is the incenter of \triangle JPL. Find m \angle MPQ.,"[IsIncenterOf(Point(S),Triangle(J,P,L))]. [Find(MeasureOf(Angle(M,P,Q)))]."
Find the perimeter of \parallelogram TRVW.,"[Find(PerimeterOf(Parallelogram(T,R,V,W)))]."
Find x.,[Find(x)].
Find y.,[Find(y)].
Each pair of polygons is similar. Find y.,"[Similar(Polygon($1),Polygon($2))]. [Find(y)]."
Find the value of x in the diagram.,[Find(x)].
"In the figure, \triangle ABC is isosceles, \triangle DCE is equilateral, and \triangle FCG is isosceles. Find the measure of the \angle 5 at vertex C.",", [Isosceles(Triangle(A,B,C))], [Equilateral(Triangle(D,C,E))] and [Isosceles(Triangle(F,C,G))]. [Find(MeasureOf(Angle(5)))], [Equals(Angle(5),Angle(C))]."
"Use rectangle LMNP, parallelogram LKMJ to solve the problem. If m \angle LMP = m \angle PMN, find m \angle PJL.","Use [Rectangle(L,M,N,P)], [Parallelogram(L,K,M,J)] to. If [Equals(MeasureOf(Angle(L,M,P)),MeasureOf(Angle(P,M,N)))], [Find(MeasureOf(Angle(P,J,L)))]."
Find the measure of \angle 1.,[Find(MeasureOf(Angle(1)))].
Find the measure of \angle 6 if AB \perp BC.,"[Find(MeasureOf(Angle(6)))] if [Perpendicular(Line(A,B),Line(B,C))]."
"In \odot R. If SU = 16.2, what is RT?","In [Circle(R)]. If [Equals(LengthOf(Line(S,U)),16.2)] [Find(LengthOf(Line(R,T)))]?"
"Find the area of the shaded sector. Round to the nearest tenth, if necessary.","[Find(AreaOf(Shaded(Sector($))))]. Round to nearest tenth, if necessary."
Find y if \triangle JLM \sim \triangle QST.,"[Find(y)] if [Similar(Triangle(J,L,M),Triangle(Q,S,T))]."
Find x.,[Find(x)].
Find z.,[Find(z)].
Find x.,[Find(x)].
Find y.,[Find(y)].
"In rhombus LMPQ, m \angle QLM = 2x^{2}-10, m \angle QPM = 8x, and MP = 10. Find m \angle LQM.","In [Rhombus(L,M,P,Q)], [Equals(MeasureOf(Angle(Q,L,M)),2x^{2}-10)] [Equals(MeasureOf(Angle(Q,P,M)),8x)] and [Equals(LengthOf(Line(M,P)),10)] [Find(MeasureOf(Angle(L,Q,M)))]."
"For the pair of similar figures, use the given areas to find x.","[Similar(Shape($1),Shape($2))], to [Find(x)]."
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
Find RS.,"[Find(LengthOf(Line(R,S)))]."
"If x = 7\sqrt{3}, find b.","If [Equals(x,7\sqrt{3})] [Find(b)]."
Find y.,[Find(y)].
Find the scale factor from W to W'.,"[Find(ScaleFactorOf(Shape(W),Shape(W')))]."
"JH, JP, and PH are midsegments of \triangle KLM. Find x.","[IsMidsegmentOf(Line(J,H),Triangle(K,L,M))], [IsMidsegmentOf(Line(J,P),Triangle(K,L,M))], [IsMidsegmentOf(Line(P,H),Triangle(K,L,M))],. [Find(x)]."
Find x to the nearest tenth. ,[Find(x)] to nearest tenth.
Find y if m \angle 5 = 68 and m \angle 3 = 3y-2.,"[Find(y)] if [Equals(MeasureOf(Angle(5)),68)] and [Equals(MeasureOf(Angle(3)),3y-2)]."
"In the figure, a \parallel b, c \parallel d, and m \angle 4 = 57. Find the measure of \angle 5.",", [Parallel(Line(a),Line(b))], [Parallel(Line(c),Line(d))] and [Equals(MeasureOf(Angle(4)),57)] [Find(MeasureOf(Angle(5)))]."
"JH, JP, and PH are midsegments of \triangle KLM. Find x.","[IsMidsegmentOf(Line(J,H),Triangle(K,L,M))], [IsMidsegmentOf(Line(J,P),Triangle(K,L,M))], [IsMidsegmentOf(Line(P,H),Triangle(K,L,M))],. [Find(x)]."
Find the perimeter of the triangle at the right. Assume that segments that appear to be tangent are tangent.,"[Find(PerimeterOf(Triangle($)))]. [Tangent(Line($),Circle($))]."
"Polygon ABCD \sim polygon AEFG, m \angle AGF = 108, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26. Find AG.","[Similar(Quadrilateral(A,B,C,D),Quadrilateral(A,E,F,G))], [Equals(MeasureOf(Angle(A,G,F)),108)] [Equals(LengthOf(Line(G,F)),14)] [Equals(LengthOf(Line(A,D)),12)] [Equals(LengthOf(Line(D,G)),4.5)] [Equals(LengthOf(Line(E,F)),8)] and [Equals(LengthOf(Line(A,B)),26)] [Find(LengthOf(Line(A,G)))]."
"For trapezoid QRTU, V and S are midpoints of the legs. If TU = 26 and SV = 17, find QR.","[Trapezoid(Q,R,T,U)], [IsMidpointOf(Point(V),LegOf(Trapezoid(Q,R,T,U)))], [IsMidpointOf(Point(S),LegOf(Trapezoid(Q,R,T,U)))],. If [Equals(LengthOf(Line(T,U)),26)] and [Equals(LengthOf(Line(S,V)),17)] [Find(LengthOf(Line(Q,R)))]."
"Find x. Round to the nearest tenth, if necessary.","[Find(x)]. Round to nearest tenth, if necessary."
AB and CB are tangent to \odot D. Find the value of x.,"[Tangent(Line(A,B),Circle(D))], [Tangent(Line(C,B),Circle(D))]. [Find(x)]."
\triangle FGH is an equilateral triangle. Find FG.,"[Equilateral(Triangle(F,G,H))] [Triangle($)]. [Find(LengthOf(Line(F,G)))]."
Find m \angle G.,[Find(MeasureOf(Angle(G)))].
"If MD = 7, find RI.","If [Equals(LengthOf(Line(M,D)),7)] [Find(LengthOf(Line(R,I)))]."
GJ is a diameter of \odot K. Find m \widehat GH.,"[IsDiameterOf(Line(G,J),Circle(K))]. [Find(MeasureOf(Arc(G,H)))]."
Find the perimeter of the triangle. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Triangle($)))]. Round to nearest tenth if necessary.
A square with side length of 9 inches is inscribed in \odot J. Find the exact circumference of \odot J.,"[Square($)], [Equals(SideOf(Square($)),9)] is inscribed in [Circle(J)]. [Find(CircumferenceOf(Circle(J)))]."
ACDF \sim VWYZ. Find x.,"[Similar(Quadrilateral(A,C,D,F),Quadrilateral(V,W,Y,Z))]. [Find(x)]."
Find the measure of \angle 3.,[Find(MeasureOf(Angle(3)))].
Quadrilateral ABCD is a rectangle. m \angle 2 = 40. Find m \angle 1.," [Rectangle(A,B,C,D)]. [Equals(MeasureOf(Angle(2)),40)] [Find(MeasureOf(Angle(1)))]."
Find m \angle C.,[Find(MeasureOf(Angle(C)))].
"Quadrilateral ABCD is a rhombus. If m \angle BCD = 54, find m \angle BAC."," [Rhombus(A,B,C,D)]. If [Equals(MeasureOf(Angle(B,C,D)),54)] [Find(MeasureOf(Angle(B,A,C)))]."
Find x.,[Find(x)].
Find y.,[Find(y)].
Find the perimeter of the triangle.,[Find(PerimeterOf(Triangle($)))].
"In \odot W, \widehat RS \cong \widehat TV. Find RS.","In [Circle(W)], [Congruent(Arc(R,S),Arc(T,V))]. [Find(LengthOf(Line(R,S)))]."
Find m \angle L.,[Find(MeasureOf(Angle(L)))].
Use the figure to find the indicated variable. Find y if m \angle 3 = 4y+30 and m \angle 7 = 7y+6.,"to. [Find(y)] if [Equals(MeasureOf(Angle(3)),4y+30)] and [Equals(MeasureOf(Angle(7)),7y+6)]."
Find the area of the shaded region. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth.
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find \angle 3.,[Find(MeasureOf(Angle(3)))].
"In the figure, m \angle 3 = 110 and m \angle 12 = 55. Find the measure of \angle 10.",", [Equals(MeasureOf(Angle(3)),110)] and [Equals(MeasureOf(Angle(12)),55)] [Find(MeasureOf(Angle(10)))]."
"In \odot O, EC and AB are diameters, and \angle BOD \cong \angle DOE \cong \angle EOF \cong \angle FOA. Find m \widehat BC.","[Circle(O)], [IsDiameterOf(Line(E,C),Circle(O))], [IsDiameterOf(Line(A,B),Circle(O))] and [Equals(Angle(B,O,D),Angle(D,O,E))], [Equals(Angle(D,O,E),Angle(E,O,F))], [Equals(Angle(E,O,F),Angle(F,O,A))]. [Find(MeasureOf(Arc(B,C)))]."
"For trapezoid QRST, A and B are midpoints of the legs. Find m \angle Q.","[Trapezoid(Q,R,S,T)], [IsMidpointOf(Point(A),LegOf(Trapezoid(Q,R,S,T)))], [IsMidpointOf(Point(B),LegOf(Trapezoid(Q,R,S,T)))],. [Find(MeasureOf(Angle(Q)))]."
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find y.,[Find(y)].
"For the pair of similar figures, find the area of the green figure.","[Similar(Shape($1),Shape($2))], [Find(AreaOf(Green(Shape($))))]."
Polygon BCDE \cong polygon RSTU. Find w.,"[Congruent(Quadrilateral(B,C,D,E),Quadrilateral(R,S,T,U))]. [Find(w)]."
Find the perimeter of the figure. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Shape($)))]. Round to nearest tenth if necessary.
"a = 8, b = 15, and c = 17, find \sin A.","[Equals(a,8)] [Equals(b,15)] and [Equals(c,17)] [Find(SinOf(Angle(A)))]."
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Each pair of polygons is similar. Find x.,"[Similar(Polygon($1),Polygon($2))]. [Find(x)]."
Find x.,[Find(x)].
Find the measure of \angle 7 if AB \perp BC.,"[Find(MeasureOf(Angle(7)))] if [Perpendicular(Line(A,B),Line(B,C))]."
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
"In \odot O, EC and AB are diameters, and \angle BOD \cong \angle DOE \cong \angle EOF \cong \angle FOA. Find m \widehat ADC.","[Circle(O)], [IsDiameterOf(Line(E,C),Circle(O))], [IsDiameterOf(Line(A,B),Circle(O))] and [Equals(Angle(B,O,D),Angle(D,O,E))], [Equals(Angle(D,O,E),Angle(E,O,F))], [Equals(Angle(E,O,F),Angle(F,O,A))]. [Find(MeasureOf(Arc(A,D,C)))]."
"parallelogram MNPQ with m \angle M = 10x and m \angle N = 20x, find \angle N.","[Parallelogram(M,N,P,Q)] with [Equals(MeasureOf(Angle(M)),10x)] and [Equals(MeasureOf(Angle(N)),20x)] [Find(MeasureOf(Angle(N)))]."
"In the figure, AB \parallel CE. If DA = 6, what is DB?",", [Parallel(Line(A,B),Line(C,E))]. If [Equals(LengthOf(Line(D,A)),6)] [Find(LengthOf(Line(D,B)))]?"
Use parallelogram ABCD to find x.,"Use [Parallelogram(A,B,C,D)] to [Find(x)]."
Find x.,[Find(x)].
Find x. Round the side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
Find m \widehat RQ.,"[Find(MeasureOf(Arc(R,Q)))]."
Find y if AD is an altitude of \triangle ABC.,"[Find(y)] if [Equals(Line(A,D),AltitudeOf(Triangle(A,B,C)))]."
Find m \angle J.,[Find(MeasureOf(Angle(J)))].
"Find ED if AB = 6, BC = 4, and AE = 9.","[Find(LengthOf(Line(E,D)))] if [Equals(LengthOf(Line(A,B)),6)] [Equals(LengthOf(Line(B,C)),4)] and [Equals(LengthOf(Line(A,E)),9)]."
Use a Pythagorean Triple to find x.,[UseTheorem(Pythagorean_Triple)] to [Find(x)].
Find m \angle E.,[Find(MeasureOf(Angle(E)))].
"In the figure, m \angle 12 = 64. Find the measure of \angle 4.",", [Equals(MeasureOf(Angle(12)),64)] [Find(MeasureOf(Angle(4)))]."
"In the figure, square WXYZ is inscribed in \odot R. Find the measure of a central angle.",", [InscribedIn(Square(W,X,Y,Z),Circle(R))]. [Find(MeasureOf(Angle($)))]."
\triangle ABC is an isosceles triangle with base BC. What is the perimeter of the triangle?,"[Isosceles(Triangle(A,B,C))], [IsBaseOf(Line(B,C),Isosceles(Triangle(A,B,C)))]. [Find(PerimeterOf(Triangle($)))]?"
"In the figure, m \angle 1 = 58, m \angle 2 = 47, and m \angle 3 = 26. Find the measure of \angle 4.",", [Equals(MeasureOf(Angle(1)),58)] [Equals(MeasureOf(Angle(2)),47)] and [Equals(MeasureOf(Angle(3)),26)] [Find(MeasureOf(Angle(4)))]."
"In \odot P, RT = 11, find m \widehat QRS. Round to the nearest hundredth.","In [Circle(P)], [Equals(LengthOf(Line(R,T)),11)] [Find(MeasureOf(Arc(Q,R,S)))]. Round to nearest hundredth."
Point S is the incenter of \triangle JPL. Find m \angle SJP.,"[IsIncenterOf(Point(S),Triangle(J,P,L))]. [Find(MeasureOf(Angle(S,J,P)))]."
Find m \angle 3.,[Find(MeasureOf(Angle(3)))].
"In A, the radius is 14 and CD = 22. Find CE."," [Circle(A)], [Equals(RadiusOf(Circle(A)),14)] and [Equals(LengthOf(Line(C,D)),22)] [Find(LengthOf(Line(C,E)))]."
Refer to the figure at the right. Find the value of m \angle BCE if p \parallel q.,"[Shape($)]. [Find(MeasureOf(Angle(B,C,E)))] if [Parallel(Line(p),Line(q))]."
Find x. Round the side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
"In \odot C, m \angle HCG = 2x and m \angle HCD = 6x+28, find m \widehat HD.","In [Circle(C)], [Equals(MeasureOf(Angle(H,C,G)),2x)] and [Equals(MeasureOf(Angle(H,C,D)),6x+28)] [Find(MeasureOf(Arc(H,D)))]."
Find x. Round the side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
ABCD \sim QSRP. Find y.,"[Similar(Quadrilateral(A,B,C,D),Quadrilateral(Q,S,R,P))]. [Find(y)]."
"Find the measure of RS of equilateral triangle RST if RS = x+9, ST = 2x, and RT = 3x-9.","[Find(LengthOf(Line(R,S)))] of [Equilateral(Triangle(R,S,T))] if [Equals(LengthOf(Line(R,S)),x+9)] [Equals(LengthOf(Line(S,T)),2x)] and [Equals(LengthOf(Line(R,T)),3x-9)]."
"The diameters of \odot A, \odot B, and \odot C are 10, 30 and 10 units, respectively. Find AZ if AZ \cong CW and CW = 2.","[Equals(DiameterOf(Circle(A)),10)] [Equals(DiameterOf(Circle(B)),30)] [Equals(DiameterOf(Circle(C)),10)] [Find(LengthOf(Line(A,Z)))] if [Equals(LengthOf(Line(A,Z)),Line(C,W))] and [Equals(LengthOf(Line(C,W)),2)]."
"If m \angle XZY = 3x+6 and m \angle XZW = 5x-12, find m \angle YXZ.","If [Equals(MeasureOf(Angle(X,Z,Y)),3x+6)] and [Equals(MeasureOf(Angle(X,Z,W)),5x-12)] [Find(MeasureOf(Angle(Y,X,Z)))]."
Find the length of CB in the isosceles triangle ABC.,"[Find(LengthOf(Line(C,B)))] in [Isosceles(Triangle(A,B,C))]."
Find x.,[Find(x)].
Find x if PS is a median of \triangle PQR.,"[Find(x)] if [IsMedianOf(Line(P,S),Triangle(P,Q,R))]."
"In \odot T, ZV = 1, and TW = 13. Find XV.","In [Circle(T)], [Equals(LengthOf(Line(Z,V)),1)] and [Equals(LengthOf(Line(T,W)),13)] [Find(LengthOf(Line(X,V)))]."
Find x.,[Find(x)].
Find x.,[Find(x)].
"Rhombus MNPQ has an area of 375 square inches. If MP is 25 inches, find NQ.","[Equals(AreaOf(Rhombus(M,N,P,Q)),375)] If [Equals(Line(M,P),25)] [Find(LengthOf(Line(N,Q)))]."
"Circles G, J, and K all intersect at L. If GH = 10, find GL.","[IntersectAt(Circle(G),Circle(J),Circle(K),Point(L))]. If [Equals(LengthOf(Line(G,H)),10)] [Find(LengthOf(Line(G,L)))]."
Find m \angle P.,[Find(MeasureOf(Angle(P)))].
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
"Find FE if AB = 6, AF = 8, BC = x, CD = y, DE = 2y-3, and FE = x+\frac{10}{3}.","[Find(LengthOf(Line(F,E)))] if [Equals(LengthOf(Line(A,B)),6)] [Equals(LengthOf(Line(A,F)),8)] [Equals(LengthOf(Line(B,C)),x)] [Equals(LengthOf(Line(C,D)),y)] [Equals(LengthOf(Line(D,E)),2y-3)] and [Equals(LengthOf(Line(F,E)),x+\frac{10}{3})]."
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Solve for x in the figure.,[Find(x)].
Find x. A = 96 in^2.,"[Find(x)]. [Equals(AreaOf(Shape(A)),96)]."
"If a = 10\sqrt{3}, find y.","If [Equals(a,10\sqrt{3})] [Find(y)]."
\triangle ABC \cong \triangle FGH. Find x.,"[Congruent(Triangle(A,B,C),Triangle(F,G,H))]. [Find(x)]."
Find z.,[Find(z)].
Use parallelogram ABCD to find m \angle DAC.,"Use [Parallelogram(A,B,C,D)] to [Find(MeasureOf(Angle(D,A,C)))]."
"If WXYZ is a kite, find YZ.","If [Kite(W,X,Y,Z)], [Find(LengthOf(Line(Y,Z)))]."
Find x.,[Find(x)].
Two triangles are similar. Find x.,"[Similar(Triangle($1),Triangle($2))]. [Find(x)]."
Find x.,[Find(x)].
Find the value of x in the diagram.,[Find(x)].
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find m \angle J.,[Find(MeasureOf(Angle(J)))].
What is the value of \tan x?,[Find(TanOf(x))]?
Find x.,[Find(x)].
Find y in the figure.,[Find(y)].
Find KL.,"[Find(LengthOf(Line(K,L)))]."
Find the angle measure of \angle 4.,[Find(MeasureOf(Angle(4)))].
"Circle W has a radius of 4 units, \odot Z has a radius of 7 units, and XY = 2. Find IC.","[Equals(RadiusOf(Circle(W)),4)] [Equals(RadiusOf(Circle(Z)),7)] and [Equals(LengthOf(Line(X,Y)),2)] [Find(LengthOf(Line(I,C)))]."
Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. Round to nearest tenth if necessary. [Tangent(Line($),Circle($))]."
"In the figure at the right, YZ is the midsegment of trapezoid TWRV. Determine the value of x.",", [IsMidsegmentOf(Line(Y,Z),Trapezoid(T,W,R,V))]. [Find(x)]."
"If PQ \cong QS, QR \cong RS, and m \angle PRS = 72, what is the measure of \angle QPS?","If [Equals(LengthOf(Line(P,Q)),Line(Q,S))], [Equals(LengthOf(Line(Q,R)),Line(R,S))] and [Equals(MeasureOf(Angle(P,R,S)),72)] [Find(MeasureOf(Angle(Q,P,S)))]?"
Use parallelogram ABCD to find y.,"Use [Parallelogram(A,B,C,D)] to [Find(y)]."
Suppose CE = 5.2 inches. Find the diameter of the circle.,"[Equals(LengthOf(Line(C,E)),5.2)] [Find(DiameterOf(Circle($)))]."
Find the area of the triangle. Round to the nearest hundredth.,[Find(AreaOf(Triangle($)))]. Round to nearest hundredth.
"In the figure, m \angle 1 = 58, m \angle 2 = 47, and m \angle 3 = 26. Find the measure of \angle 8.",", [Equals(MeasureOf(Angle(1)),58)] [Equals(MeasureOf(Angle(2)),47)] and [Equals(MeasureOf(Angle(3)),26)] [Find(MeasureOf(Angle(8)))]."
"In \triangle EDF, T is the centroid and FT = 12. Find TQ."," [Triangle(E,D,F)], [IsCentroidOf(Point(T),Triangle(E,D,F))] and [Equals(LengthOf(Line(F,T)),12)] [Find(LengthOf(Line(T,Q)))]."
Use parallelogram JKLM to find m \angle JKL if JK = 2b+3 and JM = 3a.,"Use [Parallelogram(J,K,L,M)] to [Find(MeasureOf(Angle(J,K,L)))] if [Equals(LengthOf(Line(J,K)),2b+3)] and [Equals(LengthOf(Line(J,M)),3a)]."
The orthocenter of \triangle ABC is located 6.4 units from point D. Find BC.,"orthocenter of [Triangle(A,B,C)] is located 6.4 from [Point(D)]. [Find(LengthOf(Line(B,C)))]."
Find x.,[Find(x)].
Find the measure of the altitude drawn to the hypotenuse.,"[Find(LengthOf(AltitudeOf(Triangle($1,$2,$3))))], [IsHypotenuseOf(Line($1,$3),Triangle($1,$2,$3))]."
Use parallelogram JKLM to find JK.,"Use [Parallelogram(J,K,L,M)] to [Find(LengthOf(Line(J,K)))]."
Find m \widehat VX.,"[Find(MeasureOf(Arc(V,X)))]."
Find the height of the parallelogram given its area with 100 square units.,"[Find(HeightOf(Parallelogram($)))], [Equals(AreaOf(Parallelogram($)),100)]."
Find z in the figure.,[Find(z)].
Find m \angle ACB.,"[Find(MeasureOf(Angle(A,C,B)))]."
Find the measure of \angle 1.,[Find(MeasureOf(Angle(1)))].
Find x.,[Find(x)].
"MC = 7, RM = 4, and AT = 16. Find SC.","[Equals(LengthOf(Line(M,C)),7)] [Equals(LengthOf(Line(R,M)),4)] and [Equals(LengthOf(Line(A,T)),16)] [Find(LengthOf(Line(S,C)))]."
Find x.,[Find(x)].
"If MNPQ \sim XYZW, find the perimeter of MNPQ.","If [Similar(Quadrilateral(M,N,P,Q),Quadrilateral(X,Y,Z,W))], [Find(PerimeterOf(Quadrilateral(M,N,P,Q)))]."
"For trapezoid QRST, A and B are midpoints of the legs. Find AB.","[Trapezoid(Q,R,S,T)], [IsMidpointOf(Point(A),LegOf(Trapezoid(Q,R,S,T)))], [IsMidpointOf(Point(B),LegOf(Trapezoid(Q,R,S,T)))],. [Find(LengthOf(Line(A,B)))]."
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find y in the figure.,[Find(y)].
Find x.,[Find(x)].
Find m \angle 5.,[Find(MeasureOf(Angle(5)))].
Find y.,[Find(y)].
"If KLMN is a parallelogram, find y.","If [Parallelogram(K,L,M,N)], [Find(y)]."
QS is a diameter of \odot V. Find m \widehat QRT.,"[IsDiameterOf(Line(Q,S),Circle(V))]. [Find(MeasureOf(Arc(Q,R,T)))]."
Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.,"[Find(x)] to nearest tenth. [Tangent(Line($),Circle($))]."
"If AB = 6, BC = 4, and AE = 9, find ED.","If [Equals(LengthOf(Line(A,B)),6)] [Equals(LengthOf(Line(B,C)),4)] and [Equals(LengthOf(Line(A,E)),9)] [Find(LengthOf(Line(E,D)))]."
Use parallelogram MNPR to find m \angle NRP.,"Use [Parallelogram(M,N,P,R)] to [Find(MeasureOf(Angle(N,R,P)))]."
"If WZ = 25.3, YZ = 22.4, WZ = 25.3, find XY.","If [Equals(LengthOf(Line(W,Z)),25.3)] [Equals(LengthOf(Line(Y,Z)),22.4)] [Equals(LengthOf(Line(W,Z)),25.3)] [Find(LengthOf(Line(X,Y)))]."
"In quadrilateral ABCD, AC = 188, BD = 214, m \angle BPC = 70, and P is the midpoint of AC and BD. Find the perimeter of quadrilateral ABCD.","In [Quadrilateral(A,B,C,D)], [Equals(LengthOf(Line(A,C)),188)] [Equals(LengthOf(Line(B,D)),214)] [Equals(MeasureOf(Angle(B,P,C)),70)] and [IsMidpointOf(Point(P),Line(A,C))] and [Line(B,D)]. [Find(PerimeterOf(Quadrilateral(A,B,C,D)))]."
Find the value of f in the parallelogram.,[Find(f)] in [Parallelogram($)].
Find h.,[Find(h)].
Find the measure of \angle 2 in the figure.,[Find(MeasureOf(Angle(2)))].
"If KH is parallel to JI, find the measure of \angle 1.","If [Parallel(Line(K,H),Line(J,I))], [Find(MeasureOf(Angle(1)))]."
Find the area of the shaded region. Assume that the polygon is regular unless otherwise stated. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. [Regular(Polygon($))]. Round to nearest tenth.
"a = 8, b = 15, and c = 17, find \tan A.","[Equals(a,8)] [Equals(b,15)] and [Equals(c,17)] [Find(TanOf(Angle(A)))]."
Find the area of the regular polygon. Round to the nearest tenth.,[Find(AreaOf(Regular(Polygon($))))]. Round to nearest tenth.
Find DB.,"[Find(LengthOf(Line(D,B)))]."
Find x.,[Find(x)].
Find m \angle PNM.,"[Find(MeasureOf(Angle(P,N,M)))]."
"In the figure, QR \parallel TS, QT \parallel RS, and m \angle 1 = 131. Find the measure of \angle 7.",", [Parallel(Line(Q,R),Line(T,S))], [Parallel(Line(Q,T),Line(R,S))] and [Equals(MeasureOf(Angle(1)),131)] [Find(MeasureOf(Angle(7)))]."
"Find y. Round to the nearest tenth, if necessary.","[Find(y)]. Round to nearest tenth, if necessary."
"If x = 7\sqrt{3}, find CE.","If [Equals(x,7\sqrt{3})] [Find(LengthOf(Line(C,E)))]."
"If PR \parallel KL, KN = 9, LN = 16, and PM = 2KP, find KP.","If [Parallel(Line(P,R),Line(K,L))], [Equals(LengthOf(Line(K,N)),9)] [Equals(LengthOf(Line(L,N)),16)] and [Equals(LengthOf(Line(P,M)),Mul(Line(K,P),2))], [Find(LengthOf(Line(K,P)))]."
Find z.,[Find(z)].
"WXYZ is a kite. If m \angle WXY = 120, m \angle WZY = 4x, and m \angle ZWX = 10x, find m \angle ZYX."," [Kite(W,X,Y,Z)]. If [Equals(MeasureOf(Angle(W,X,Y)),120)] [Equals(MeasureOf(Angle(W,Z,Y)),4x)] and [Equals(MeasureOf(Angle(Z,W,X)),10x)] [Find(MeasureOf(Angle(Z,Y,X)))]."
"In the figure, m \angle 11 = 62 and m \angle 14 = 38. Find the measure of \angle 2.",", [Equals(MeasureOf(Angle(11)),62)] and [Equals(MeasureOf(Angle(14)),38)] [Find(MeasureOf(Angle(2)))]."
"If LK = 4, MP = 3, PQ = 6, KJ = 2, RS = 6, and LP = 2, find QK.","If [Equals(LengthOf(Line(L,K)),4)] [Equals(LengthOf(Line(M,P)),3)] [Equals(LengthOf(Line(P,Q)),6)] [Equals(LengthOf(Line(K,J)),2)] [Equals(LengthOf(Line(R,S)),6)] and [Equals(LengthOf(Line(L,P)),2)] [Find(LengthOf(Line(Q,K)))]."
Find m \angle 3.,[Find(MeasureOf(Angle(3)))].
"If MNPQ \sim XYZW, find the perimeter of XYZW.","If [Similar(Quadrilateral(M,N,P,Q),Quadrilateral(X,Y,Z,W))], [Find(PerimeterOf(Quadrilateral(X,Y,Z,W)))]."
Find the value of the variable x in the figure.,[Find(x)].
Find CP.,"[Find(LengthOf(Line(C,P)))]."
Find m \angle Y.,[Find(MeasureOf(Angle(Y)))].
"In the figure, m \angle 9 = 75. Find the measure of \angle 8.",", [Equals(MeasureOf(Angle(9)),75)] [Find(MeasureOf(Angle(8)))]."
Find m \angle ZXY.,"[Find(MeasureOf(Angle(Z,X,Y)))]."
"If DE = 60 and FC = 16, find AB.","If [Equals(LengthOf(Line(D,E)),60)] and [Equals(LengthOf(Line(F,C)),16)] [Find(LengthOf(Line(A,B)))]."
"In \triangle EFG, HL \parallel EF, EH = 9, HG = 21, and FL = 6. Find LG.","In [Triangle(E,F,G)], [Parallel(Line(H,L),Line(E,F))], [Equals(LengthOf(Line(E,H)),9)] [Equals(LengthOf(Line(H,G)),21)] and [Equals(LengthOf(Line(F,L)),6)] [Find(LengthOf(Line(L,G)))]."
Find the measure of \angle 2.,[Find(MeasureOf(Angle(2)))].
Find x.,[Find(x)].
m \angle 4 = 32. Find the measure of \angle 5.,"[Equals(MeasureOf(Angle(4)),32)] [Find(MeasureOf(Angle(5)))]."
Find the ratio of the area of the circle to the area of the square.,"[Find(RatioOf(AreaOf(Circle($)),AreaOf(Square($))))]."
"QRST is a rectangle. If QP = 3x+11 and PS = 4x+8, find QS."," [Rectangle(Q,R,S,T)]. If [Equals(LengthOf(Line(Q,P)),3x+11)] and [Equals(LengthOf(Line(P,S)),4x+8)] [Find(LengthOf(Line(Q,S)))]."
Find the area of the blue region.,[Find(AreaOf(Blue(Shape($))))].
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
"Use rectangle LMNP, parallelogram LKMJ to solve the problem. If m \angle MJN = 35, find m \angle MPN.","Use [Rectangle(L,M,N,P)], [Parallelogram(L,K,M,J)] to. If [Equals(MeasureOf(Angle(M,J,N)),35)] [Find(MeasureOf(Angle(M,P,N)))]."
Find x. Round side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
"For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure.","[Similar(Shape($1),Shape($2))], to [Find(ScaleFactorOf(Blue(Shape($)),Green(Shape($))))]."
"The area of \parallelogram ABCD is 150 square meters. The area of \parallelogram FGHJ is 54 square meters. If \parallelogram ABCD \sim \parallelogram FGHJ, find the scale factor of \parallelogram FGHJ to \parallelogram ABCD.","[Equals(AreaOf(Parallelogram(A,B,C,D)),150)] [Equals(AreaOf(Parallelogram(F,G,H,J)),54)] If [Similar(Parallelogram(A,B,C,D),Parallelogram(F,G,H,J))], [Find(ScaleFactorOf(Parallelogram(F,G,H,J),Parallelogram(A,B,C,D)))]."
"For the pair of similar figures, use the given areas to find the scale factor from the blue to the green figure.","[Similar(Shape($1),Shape($2))], to [Find(ScaleFactorOf(Blue(Shape($)),Green(Shape($))))]."
"Find AC if AC = x-3, BE = 20, AB = 16, and CD = x+5.","[Find(LengthOf(Line(A,C)))] if [Equals(LengthOf(Line(A,C)),x-3)] [Equals(LengthOf(Line(B,E)),20)] [Equals(LengthOf(Line(A,B)),16)] and [Equals(LengthOf(Line(C,D)),x+5)]."
Find the area of the figure.,[Find(AreaOf(Shape($)))].
"For trapezoid RSTV, A and B are midpoints of the legs. Find VT.","[Trapezoid(R,S,T,V)], [IsMidpointOf(Point(A),LegOf(Trapezoid(R,S,T,V)))], [IsMidpointOf(Point(B),LegOf(Trapezoid(R,S,T,V)))],. [Find(LengthOf(Line(V,T)))]."
"In the figure, CP is an altitude, CQ is the angle bisector of \angle ACB, and R is the midpoint of AB. Find AB if AR = 3x+6 and RB = 5x-14.",", [IsAltitudeOf(Line(C,P),Shape($))], [BisectsAngle(Line(C,Q),Angle(A,C,B))] and [IsMidpointOf(Point(R),Line(A,B))]. [Find(LengthOf(Line(A,B)))] if [Equals(LengthOf(Line(A,R)),3x+6)] and [Equals(LengthOf(Line(R,B)),5x-14)]."
"If QR \parallel XY, XQ = 15, QZ = 12, and YR = 20, what is the length of RZ.","If [Parallel(Line(Q,R),Line(X,Y))], [Equals(LengthOf(Line(X,Q)),15)] [Equals(LengthOf(Line(Q,Z)),12)] and [Equals(LengthOf(Line(Y,R)),20)] [Find(LengthOf(Line(R,Z)))]."
"In \odot G, m \angle AGB = 30 and CG \perp GD. Find m \widehat CDF.","In [Circle(G)], [Equals(MeasureOf(Angle(A,G,B)),30)] and [Perpendicular(Line(C,G),Line(G,D))]. [Find(MeasureOf(Arc(C,D,F)))]."
"If PR \parallel WX, WX = 10, XY = 6, WY = 8, RY = 5, and PS = 3, find PQ.","If [Parallel(Line(P,R),Line(W,X))], [Equals(LengthOf(Line(W,X)),10)] [Equals(LengthOf(Line(X,Y)),6)] [Equals(LengthOf(Line(W,Y)),8)] [Equals(LengthOf(Line(R,Y)),5)] and [Equals(LengthOf(Line(P,S)),3)] [Find(LengthOf(Line(P,Q)))]."
Find m \angle 3.,[Find(MeasureOf(Angle(3)))].
"If GH \cong HK, HJ \cong YK, and m \angle GJK = 100, what is the measure of \angle HGK?","If [Equals(LengthOf(Line(G,H)),Line(H,K))], [Equals(LengthOf(Line(H,J)),Line(Y,K))] and [Equals(MeasureOf(Angle(G,J,K)),100)] [Find(MeasureOf(Angle(H,G,K)))]?"
Find MN.,"[Find(LengthOf(Line(M,N)))]."
Find x.,[Find(x)].
Find the measure of the altitude drawn to the hypotenuse.,"[Find(LengthOf(AltitudeOf(Triangle($1,$2,$3))))], [IsHypotenuseOf(Line($1,$3),Triangle($1,$2,$3))]."
"isosceles trapezoid TWYZ with \angle Z \cong \angle Y, m \angle Z = 30x, \angle T \cong \angle W, and m \angle T = 20x, find \angle W.","[Isosceles(Trapezoid(T,W,Y,Z))] with [Equals(Angle(Z),Angle(Y))], [Equals(MeasureOf(Angle(Z)),30x)] [Equals(Angle(T),Angle(W))] and [Equals(MeasureOf(Angle(T)),20x)] [Find(MeasureOf(Angle(W)))]."
Find m \angle Q.,[Find(MeasureOf(Angle(Q)))].
"In \odot F, GK = 14 and m \widehat GHK = 142. Find m \widehat GH.","In [Circle(F)], [Equals(LengthOf(Line(G,K)),14)] and [Equals(MeasureOf(Arc(G,H,K)),142)] [Find(MeasureOf(Arc(G,H)))]."
Find QX if EX = 24 and DE = 7.,"[Find(LengthOf(Line(Q,X)))] if [Equals(LengthOf(Line(E,X)),24)] and [Equals(LengthOf(Line(D,E)),7)]."
Find the perimeter of the triangle.,[Find(PerimeterOf(Triangle($)))].
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
"If QR \parallel XY, XQ \cong QZ, and QR = 9.5 units, what is the length of XY.","If [Parallel(Line(Q,R),Line(X,Y))], [Equals(LengthOf(Line(X,Q)),Line(Q,Z))] and [Equals(LengthOf(Line(Q,R)),9.5)] [Find(LengthOf(Line(X,Y)))]."
"If \triangle JKL \sim \triangle PQR and the area of \triangle JKL is 30 square inches, find the area of \triangle PQR.","If [Similar(Triangle(J,K,L),Triangle(P,Q,R))] and [Equals(AreaOf(Triangle(J,K,L)),30)] [Find(AreaOf(Triangle(P,Q,R)))]."
Find m \widehat DH.,"[Find(MeasureOf(Arc(D,H)))]."
"Find the perimeter of the figure in feet. Round to the nearest tenth, if necessary.","[Find(PerimeterOf(Shape($)))] in. Round to nearest tenth, if necessary."
"RSTV is a trapezoid with bases RV and ST and median MN. Find x if MN = 60, ST = 4x-1, and RV = 6x+11."," [IsBaseOf(Line(R,V),Trapezoid(R,S,T,V))], [IsBaseOf(Line(S,T),Trapezoid(R,S,T,V))], [IsMedianOf(Line(M,N),Trapezoid(R,S,T,V))]. [Find(x)] if [Equals(LengthOf(Line(M,N)),60)] [Equals(LengthOf(Line(S,T)),4x-1)] and [Equals(LengthOf(Line(R,V)),6x+11)]."
Refer to the triangle shown below. Find x to the nearest tenth.,[Triangle($)]. [Find(x)] to nearest tenth.
Solve for x.,[Find(x)].
QS is a diameter of \odot V. Find m \widehat PQR.,"[IsDiameterOf(Line(Q,S),Circle(V))]. [Find(MeasureOf(Arc(P,Q,R)))]."
Find x.,[Find(x)].
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
Find the perimeter of the triangle. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Triangle($)))]. Round to nearest tenth if necessary.
"If \angle RST is a right angle, SU \perp RT, UV \perp ST, and m \angle RTS = 47, find m \angle R.","If [RightAngle(Angle(R,S,T))], [Perpendicular(Line(S,U),Line(R,T))], [Perpendicular(Line(U,V),Line(S,T))] and [Equals(MeasureOf(Angle(R,T,S)),47)] [Find(MeasureOf(Angle(R)))]."
Find x so that p \parallel q.,"[Find(x)] so [Parallel(Line(p),Line(q))]."
"Find x if AC = x-3, BE = 20, AB = 16, and CD = x+5.","[Find(x)] if [Equals(LengthOf(Line(A,C)),x-3)] [Equals(LengthOf(Line(B,E)),20)] [Equals(LengthOf(Line(A,B)),16)] and [Equals(LengthOf(Line(C,D)),x+5)]."
Find m \angle DBA.,"[Find(MeasureOf(Angle(D,B,A)))]."
Find x.,[Find(x)].
Find x.,[Find(x)].
Find x.,[Find(x)].
Find m \angle 5.,[Find(MeasureOf(Angle(5)))].
"In the figure, JM \cong PM and ML \cong PL. If m \angle PLJ = 34, find m \angle JPM.",", [Equals(LengthOf(Line(J,M)),Line(P,M))] and [Equals(LengthOf(Line(M,L)),Line(P,L))]. If [Equals(MeasureOf(Angle(P,L,J)),34)] [Find(MeasureOf(Angle(J,P,M)))]."
"In \odot G, m \angle AGB = 30 and CG \perp GD. Find m \widehat BCD.","In [Circle(G)], [Equals(MeasureOf(Angle(A,G,B)),30)] and [Perpendicular(Line(C,G),Line(G,D))]. [Find(MeasureOf(Arc(B,C,D)))]."
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find the exact circumference of the circle.,[Find(CircumferenceOf(Circle($)))].
"Circle O has a radius of 10, AB = 10 and m \overrightarrow AB = 60. Find m \widehat OX.","[Equals(RadiusOf(Circle(O)),10)] [Equals(LengthOf(Line(A,B)),10)] and [Equals(LengthOf(Line(A,B)),60)] [Find(MeasureOf(Arc(O,X)))]."
Find z in the figure.,[Find(z)].
"In \odot F, GK = 14 and m \widehat GHK = 142. Find JK.","In [Circle(F)], [Equals(LengthOf(Line(G,K)),14)] and [Equals(MeasureOf(Arc(G,H,K)),142)] [Find(LengthOf(Line(J,K)))]."
Find y.,[Find(y)].
"In the figure, QR \parallel TS, QT \parallel RS, and m \angle 1 = 131. Find the measure of \angle 5.",", [Parallel(Line(Q,R),Line(T,S))], [Parallel(Line(Q,T),Line(R,S))] and [Equals(MeasureOf(Angle(1)),131)] [Find(MeasureOf(Angle(5)))]."
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find x.,[Find(x)].
Find the value of the variable x in the figure.,[Find(x)].
"In \odot F, if DA = 7.4, what is EF?","In [Circle(F)], if [Equals(LengthOf(Line(D,A)),7.4)] [Find(LengthOf(Line(E,F)))]?"
Express the ratio of \tan V as a decimal to the nearest hundredth.,[Find(RatioOf(TanOf(Angle(V))))] to nearest hundredth.
"In \triangle PQR, RS = 3 and QS = 14. Find PS.","In [Triangle(P,Q,R)], [Equals(LengthOf(Line(R,S)),3)] and [Equals(LengthOf(Line(Q,S)),14)] [Find(LengthOf(Line(P,S)))]."
Find x.,[Find(x)].
Find y.,[Find(y)].
Find x.,[Find(x)].
"In \triangle GHJ, HP = 5x-16, PJ = 3x+8, m \angle GJN = 6y-3, m \angle NJH = 4y+23 and m \angle HMG = 4z+14. Find m \angle GJH if JN is an angle bisector.","In [Triangle(G,H,J)], [Equals(LengthOf(Line(H,P)),5x-16)] [Equals(LengthOf(Line(P,J)),3x+8)] [Equals(MeasureOf(Angle(G,J,N)),6y-3)] [Equals(MeasureOf(Angle(N,J,H)),4y+23)] and [Equals(MeasureOf(Angle(H,M,G)),4z+14)] [Find(MeasureOf(Angle(G,J,H)))] if [BisectsAngle(Line(J,N),Angle($))]."
"JKLM is a rectangle. MLPR is a rhombus. \angle JMK \cong \angle RMP, m \angle JMK = 55 and m \angle MRP = 70. Find m \angle MPR."," [Rectangle(J,K,L,M)]. [Rhombus(M,L,P,R)]. [Equals(Angle(J,M,K),Angle(R,M,P))], [Equals(MeasureOf(Angle(J,M,K)),55)] and [Equals(MeasureOf(Angle(M,R,P)),70)] [Find(MeasureOf(Angle(M,P,R)))]."
Trapezoid ABCD has an area of 750 square meters. Find the height of ABCD.,"[Equals(AreaOf(Trapezoid(A,B,C,D)),750)] [Find(HeightOf(Quadrilateral(A,B,C,D)))]."
"In \odot F, FH \cong FL and FK = 17. Find JH.","In [Circle(F)], [Equals(LengthOf(Line(F,H)),Line(F,L))] and [Equals(LengthOf(Line(F,K)),17)] [Find(LengthOf(Line(J,H)))]."
Find y.,[Find(y)].
\triangle RSV \cong \triangle TVS. Find y.,"[Congruent(Triangle(R,S,V),Triangle(T,V,S))]. [Find(y)]."
"Chords JF and BC intersect at K. If BK = 8, KC = 12, and KF = 16, find JK.","[IsChordOf(Line(J,F),Circle($))], [IsChordOf(Line(B,C),Circle($))]. [IntersectAt(Line(J,F),Line(B,C),Point(K))]. If [Equals(LengthOf(Line(B,K)),8)] [Equals(LengthOf(Line(K,C)),12)] and [Equals(LengthOf(Line(K,F)),16)] [Find(LengthOf(Line(J,K)))]."
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Find HJ.,"[Find(LengthOf(Line(H,J)))]."
Express the ratio of \cos Q as a decimal to the nearest hundredth.,[Find(RatioOf(CosOf(Angle(Q))))] to nearest hundredth.
"If WXYZ is a kite, find ZY.","If [Kite(W,X,Y,Z)], [Find(LengthOf(Line(Z,Y)))]."
Find x.,[Find(x)].
Find LP.,"[Find(LengthOf(Line(L,P)))]."
Find \angle V.,[Find(MeasureOf(Angle(V)))].
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
"For the pair of similar figures, find the area of the green figure.","[Similar(Shape($1),Shape($2))], [Find(AreaOf(Green(Shape($))))]."
Find x so that m \parallel n.,"[Find(x)] so [Parallel(Line(m),Line(n))]."
Find x.,[Find(x)].
Find RT.,"[Find(LengthOf(Line(R,T)))]."
"Quadrilateral ABCD is inscribed in \odot Z such that m \angle BZA = 104, m \widehat CB = 94, and AB \parallel DC. Find m \widehat BA.","[InscribedIn(Quadrilateral(A,B,C,D),Circle(Z))] [Equals(MeasureOf(Angle(B,Z,A)),104)] [Equals(MeasureOf(Arc(C,B)),94)] and [Parallel(Line(A,B),Line(D,C))]. [Find(MeasureOf(Arc(B,A)))]."
Use parallelogram MNPR to find m \angle MQN.,"Use [Parallelogram(M,N,P,R)] to [Find(MeasureOf(Angle(M,Q,N)))]."
"If KH is parallel to JI, find the measure of \angle 2.","If [Parallel(Line(K,H),Line(J,I))], [Find(MeasureOf(Angle(2)))]."
Find x. Round the angle measure to the nearest degree.,[Find(x)]. Round angle measure to nearest degree.
"In the figure, m \angle 1 = 94. Find the measure of \angle 5.",", [Equals(MeasureOf(Angle(1)),94)] [Find(MeasureOf(Angle(5)))]."
Find x if AD is a median of \triangle ABC.,"[Find(x)] if [IsMedianOf(Line(A,D),Triangle(A,B,C))]."
Find x.,[Find(x)].
Find x in the figure.,[Find(x)].
Express the ratio of \sin Q as a decimal to the nearest hundredth.,[Find(RatioOf(SinOf(Angle(Q))))] to nearest hundredth.
Find m \angle 3.,[Find(MeasureOf(Angle(3)))].
Find y.,[Find(y)].
Find x.,[Find(x)].
"Use rhombus ABCD with m \angle 1 = 2x+20, m \angle 2 = 5x-4, AC = 15, and m \angle 3 = y^{2}+26. Find AF.","Use [Rhombus(A,B,C,D)] with [Equals(MeasureOf(Angle(1)),2x+20)] [Equals(MeasureOf(Angle(2)),5x-4)] [Equals(LengthOf(Line(A,C)),15)] and [Equals(MeasureOf(Angle(3)),y^{2}+26)] [Find(LengthOf(Line(A,F)))]."
Use a Pythagorean Triple to find x.,[UseTheorem(Pythagorean_Triple)] to [Find(x)].
Find m \angle MRQ so that a \parallel b.,"[Find(MeasureOf(Angle(M,R,Q)))] so [Parallel(Line(a),Line(b))]."
Find the variable of q to the nearest tenth. Assume that segments that appear to be tangent are tangent.,"[Find(q)] to nearest tenth. [Tangent(Line($),Circle($))]."
Find x.,[Find(x)].
"Given a \parallel b, find m \angle 1.","[Parallel(Line(a),Line(b))], [Find(MeasureOf(Angle(1)))]."
Find x. Round to the nearest tenth if necessary.,[Find(x)]. Round to nearest tenth if necessary.
Find JK.,"[Find(LengthOf(Line(J,K)))]."
Find x.,[Find(x)].
Find m \angle 5.,[Find(MeasureOf(Angle(5)))].
"For the pair of similar figures, use the given areas to find x.","[Similar(Shape($1),Shape($2))], to [Find(x)]."
Triangle JKL is circumscribed about \odot R. Find the perimeter of \triangle JKL.,"[CircumscribedTo(Triangle(J,K,L),Circle(R))]. [Find(PerimeterOf(Triangle(J,K,L)))]."
Find x.,[Find(x)].
Find x in the figure.,[Find(x)].
"Find the area of the shaded sector. Round to the nearest tenth, if necessary.","[Find(AreaOf(Shaded(Sector($))))]. Round to nearest tenth, if necessary."
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
A regular hexagon is inscribed in a circle with a diameter of 14. Find the area of the red segment.,"[InscribedIn(Regular(Hexagon($)),Circle($))], [Equals(DiameterOf(Circle($)),14)] [Find(AreaOf(Red(Line($))))]."
Quadrilateral MNOP is a rhombus. Find m \angle MRN.," [Rhombus(M,N,O,P)]. [Find(MeasureOf(Angle(M,R,N)))]."
Find the measure of the altitude drawn to the hypotenuse.,"[Find(LengthOf(AltitudeOf(Triangle($1,$2,$3))))], [IsHypotenuseOf(Line($1,$3),Triangle($1,$2,$3))]."
"Use rhombus XYZW with m \angle WYZ = 53, VW = 3, XV = 2a-2, and ZV = \frac{5a+1}{4}. Find m \angle YZV.","Use [Rhombus(X,Y,Z,W)] with [Equals(MeasureOf(Angle(W,Y,Z)),53)] [Equals(LengthOf(Line(V,W)),3)] [Equals(LengthOf(Line(X,V)),2a-2)] and [Equals(LengthOf(Line(Z,V)),\frac{5a+1}{4})] [Find(MeasureOf(Angle(Y,Z,V)))]."
Find m \angle B.,[Find(MeasureOf(Angle(B)))].
"Circle L has a radius of 32 centimeters. LH \perp GJ, and GJ = 40 centimeters. Find LK.","[Equals(RadiusOf(Circle(L)),32)] [Perpendicular(Line(L,H),Line(G,J))] and [Equals(LengthOf(Line(G,J)),40)] [Find(LengthOf(Line(L,K)))]."
Find x.,[Find(x)].
Find the value of the variable y in the figure.,[Find(y)].
What is the value of x in the figure below?,[Find(x)]?
Find y.,[Find(y)].
Find the area of the kite.,[Find(AreaOf(Kite($)))].
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
"If PR \parallel WX, WX = 10, XY = 6, WY = 8, RY = 5, and PS = 3, find SY.","If [Parallel(Line(P,R),Line(W,X))], [Equals(LengthOf(Line(W,X)),10)] [Equals(LengthOf(Line(X,Y)),6)] [Equals(LengthOf(Line(W,Y)),8)] [Equals(LengthOf(Line(R,Y)),5)] and [Equals(LengthOf(Line(P,S)),3)] [Find(LengthOf(Line(S,Y)))]."
Find \angle 4.,[Find(MeasureOf(Angle(4)))].
\triangle MHJ \cong \triangle PQJ. Find y.,"[Congruent(Triangle(M,H,J),Triangle(P,Q,J))]. [Find(y)]."
What is the length of RT?,"[Find(LengthOf(Line(R,T)))]?"
Find the area of the kite.,[Find(AreaOf(Kite($)))].
"In the figure, m \angle 12 = 64. Find the measure of \angle 5.",", [Equals(MeasureOf(Angle(12)),64)] [Find(MeasureOf(Angle(5)))]."
Find x. Round side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
Find m \angle MRP.,"[Find(MeasureOf(Angle(M,R,P)))]."
Find the area of the triangle. Round to the nearest tenth if necessary.,[Find(AreaOf(Triangle($)))]. Round to nearest tenth if necessary.
"If TU \perp UV and UV \perp VW, find m \angle 1.","If [Perpendicular(Line(T,U),Line(U,V))] and [Perpendicular(Line(U,V),Line(V,W))], [Find(MeasureOf(Angle(1)))]."
Find m \angle 1 in the figure.,[Find(MeasureOf(Angle(1)))].
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
"ABCD is a trapezoid. If m \angle ABC = 4x+11 and m \angle DAB = 2x+33, find the value of x so that ABCD is isosceles."," [Trapezoid(A,B,C,D)]. If [Equals(MeasureOf(Angle(A,B,C)),4x+11)] and [Equals(MeasureOf(Angle(D,A,B)),2x+33)] [Find(x)] so [Isosceles(Quadrilateral(A,B,C,D))]."
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find the exact circumference of \odot P.,[Find(CircumferenceOf(Circle(P)))].
Find y.,[Find(y)].
Find h in the triangle.,[Find(h)] in [Triangle($)].
Find the area of the regular polygon. Round to the nearest tenth.,[Find(AreaOf(Regular(Polygon($))))]. Round to nearest tenth.
Find y.,[Find(y)].
"The area of \parallelogram ABCD is 150 square meters. The area of \parallelogram FGHJ is 54 square meters. If \parallelogram ABCD \sim \parallelogram FGHJ, find the value of x.","[Equals(AreaOf(Parallelogram(A,B,C,D)),150)] [Equals(AreaOf(Parallelogram(F,G,H,J)),54)] If [Similar(Parallelogram(A,B,C,D),Parallelogram(F,G,H,J))], [Find(x)]."
Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. [Regular(Polygon($))]. Round to nearest tenth.
"If b = 18, find a.","If [Equals(b,18)] [Find(a)]."
"ABCD is a rhombus. If EB = 9, AB = 12 and m \angle ABD = 55. Find m \angle ACB."," [Rhombus(A,B,C,D)]. If [Equals(LengthOf(Line(E,B)),9)] [Equals(LengthOf(Line(A,B)),12)] and [Equals(MeasureOf(Angle(A,B,D)),55)] [Find(MeasureOf(Angle(A,C,B)))]."
PQ is tangent to circles R and S. Find PQ.,"[Tangent(Line(P,Q),Circle(R))] and [Circle(S)]. [Find(LengthOf(Line(P,Q)))]."
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find h.,[Find(h)].
Find m \angle Y.,[Find(MeasureOf(Angle(Y)))].
"If m \angle 1 = 3x+40, m \angle 2 = 2(y-10), and m \angle 3 = 2x+70, find y.","If [Equals(MeasureOf(Angle(1)),3x+40)] [Equals(MeasureOf(Angle(2)),2(y-10))] and [Equals(MeasureOf(Angle(3)),2x+70)] [Find(y)]."
"In \odot S, find PR.","In [Circle(S)], [Find(LengthOf(Line(P,R)))]."
"If m \widehat FE = 118, m \widehat AB = 108, m \angle EGB = 52, and m \angle EFB = 30. Find m \widehat AC.","If [Equals(MeasureOf(Arc(F,E)),118)] [Equals(MeasureOf(Arc(A,B)),108)] [Equals(MeasureOf(Angle(E,G,B)),52)] and [Equals(MeasureOf(Angle(E,F,B)),30)] [Find(MeasureOf(Arc(A,C)))]."
Use parallelogram ABCD to find CD.,"Use [Parallelogram(A,B,C,D)] to [Find(LengthOf(Line(C,D)))]."
Find HK.,"[Find(LengthOf(Line(H,K)))]."
Find the variable of c to the nearest tenth. Assume that segments that appear to be tangent are tangent.,"[Find(c)] to nearest tenth. [Tangent(Line($),Circle($))]."
Find y.,[Find(y)].
Find x.,[Find(x)].
Find z.,[Find(z)].
"If BT = 5 and TC = 8, find CD.","If [Equals(LengthOf(Line(B,T)),5)] and [Equals(LengthOf(Line(T,C)),8)] [Find(LengthOf(Line(C,D)))]."
"In \odot A, m \angle EAD = 42. Find m \widehat CD.","In [Circle(A)], [Equals(MeasureOf(Angle(E,A,D)),42)] [Find(MeasureOf(Arc(C,D)))]."
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find the measure of \angle 6.,[Find(MeasureOf(Angle(6)))].
"a = 8, b = 15, and c = 17, find \cos B.","[Equals(a,8)] [Equals(b,15)] and [Equals(c,17)] [Find(CosOf(Angle(B)))]."
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find the measure of \angle 1 if m \angle 4 = m \angle 5.,"[Find(MeasureOf(Angle(1)))] if [Equals(MeasureOf(Angle(4)),MeasureOf(Angle(5)))]."
"Points S, T, and U are the midpoints of DE, EF, and DF, respectively. Find x.","[IsMidpointOf(Point(S),Line(D,E))], [IsMidpointOf(Point(T),Line(E,F))], [IsMidpointOf(Point(U),Line(D,F))],,. [Find(x)]."
"In \triangle PQR, ZQ = 3a-11, ZP = a+5, PY = 2c-1, YR = 4c-11, m \angle PRZ = 4b-17, m \angle ZRQ = 3b-4, m \angle QYR = 7b+6, and m \angle PXR = 2a+10. Find PR if QY is a median.","In [Triangle(P,Q,R)], [Equals(LengthOf(Line(Z,Q)),3a-11)] [Equals(LengthOf(Line(Z,P)),a+5)] [Equals(LengthOf(Line(P,Y)),2c-1)] [Equals(LengthOf(Line(Y,R)),4c-11)] [Equals(MeasureOf(Angle(P,R,Z)),4b-17)] [Equals(MeasureOf(Angle(Z,R,Q)),3b-4)] [Equals(MeasureOf(Angle(Q,Y,R)),7b+6)] and [Equals(MeasureOf(Angle(P,X,R)),2a+10)] [Find(LengthOf(Line(P,R)))] if [IsMedianOf(Line(Q,Y),Shape($))]."
Triangle JKL is circumscribed about \odot R. Find x.,"[CircumscribedTo(Triangle(J,K,L),Circle(R))]. [Find(x)]."
"Quadrilateral DEFG is a rectangle. If FD = 3x-7 and EG = x+5, find EG."," [Rectangle(D,E,F,G)]. If [Equals(LengthOf(Line(F,D)),3x-7)] and [Equals(LengthOf(Line(E,G)),x+5)] [Find(LengthOf(Line(E,G)))]."
Find the area of the triangle. Round to the nearest tenth if necessary.,[Find(AreaOf(Triangle($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Each pair of polygons is similar. Find y.,"[Similar(Polygon($1),Polygon($2))]. [Find(y)]."
"For isosceles trapezoid XYZW, find m \angle Z.","For [Isosceles(Trapezoid(X,Y,Z,W))], [Find(MeasureOf(Angle(Z)))]."
"WXYZ is a square. If WT = 3, find ZX."," [Square(W,X,Y,Z)]. If [Equals(LengthOf(Line(W,T)),3)] [Find(LengthOf(Line(Z,X)))]."
Find x.,[Find(x)].
Find the area of the shaded sector. Round to the nearest tenth.,[Find(AreaOf(Shaded(Sector($))))]. Round to nearest tenth.
"For trapezoid QRTU, V and S are midpoints of the legs. If VS = 9 and UT = 12, find QR.","[Trapezoid(Q,R,T,U)], [IsMidpointOf(Point(V),LegOf(Trapezoid(Q,R,T,U)))], [IsMidpointOf(Point(S),LegOf(Trapezoid(Q,R,T,U)))],. If [Equals(LengthOf(Line(V,S)),9)] and [Equals(LengthOf(Line(U,T)),12)] [Find(LengthOf(Line(Q,R)))]."
Find x.,[Find(x)].
"The diameters of \odot A, \odot B, and \odot C are 8 inches, 18 inches, and 11 inches, respectively. Find FG.","[Equals(DiameterOf(Circle(A)),8)] [Equals(DiameterOf(Circle(B)),18)] [Equals(DiameterOf(Circle(C)),11)] [Find(LengthOf(Line(F,G)))]."
Find x.,[Find(x)].
Find the value of x.,[Find(x)].
"In the figure, QR \parallel TS, QT \parallel RS, and m \angle 1 = 131. Find the measure of \angle 2.",", [Parallel(Line(Q,R),Line(T,S))], [Parallel(Line(Q,T),Line(R,S))] and [Equals(MeasureOf(Angle(1)),131)] [Find(MeasureOf(Angle(2)))]."
"If CDFG is a kite, find GF.","If [Kite(C,D,F,G)], [Find(LengthOf(Line(G,F)))]."
"For the pair of similar figures, use the given areas to find x.","[Similar(Shape($1),Shape($2))], to [Find(x)]."
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
Find x.,[Find(x)].
"If PR \parallel WX, WX = 10, XY = 6, WY = 8, RY = 5, and PS = 3, find SY.","If [Parallel(Line(P,R),Line(W,X))], [Equals(LengthOf(Line(W,X)),10)] [Equals(LengthOf(Line(X,Y)),6)] [Equals(LengthOf(Line(W,Y)),8)] [Equals(LengthOf(Line(R,Y)),5)] and [Equals(LengthOf(Line(P,S)),3)] [Find(LengthOf(Line(S,Y)))]."
"If J, P, and L are the midpoints of KH, HM and MK, respectively. Find y.","If [IsMidpointOf(Point(J),Line(K,H))], [IsMidpointOf(Point(P),Line(H,M))], [IsMidpointOf(Point(L),Line(M,K))],,. [Find(y)]."
Find y.,[Find(y)].
Find x.,[Find(x)].
Find m \angle K.,[Find(MeasureOf(Angle(K)))].
"WXYZ is a kite. If m \angle WXY = 13x+24, m \angle WZY = 35, and m \angle ZWX = 13x+14, find m \angle ZYX."," [Kite(W,X,Y,Z)]. If [Equals(MeasureOf(Angle(W,X,Y)),13x+24)] [Equals(MeasureOf(Angle(W,Z,Y)),35)] and [Equals(MeasureOf(Angle(Z,W,X)),13x+14)] [Find(MeasureOf(Angle(Z,Y,X)))]."
"If a = 4, find b.","If [Equals(a,4)] [Find(b)]."
Find JL.,"[Find(LengthOf(Line(J,L)))]."
Find the perimeter of the figure. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Shape($)))]. Round to nearest tenth if necessary.
Find y.,[Find(y)].
Find x.,[Find(x)].
"If TU = 14, what it the radius of \odot Q.","If [Equals(LengthOf(Line(T,U)),14)] [Find(RadiusOf(Circle(Q)))]."
Find \angle 6.,[Find(MeasureOf(Angle(6)))].
Find x.,[Find(x)].
Find x so that m \parallel n.,"[Find(x)] so [Parallel(Line(m),Line(n))]."
Find the area of the shaded region. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth.
Find m \angle AEB.,"[Find(MeasureOf(Angle(A,E,B)))]."
Find XA.,"[Find(LengthOf(Line(X,A)))]."
The segment is tangent to the circle. Find x.,"[Tangent(Line($),Circle($))] to [Circle($)]. [Find(x)]."
"For the pair of similar figures, find the area of the green figure.","[Similar(Shape($1),Shape($2))], [Find(AreaOf(Green(Shape($))))]."
"In \triangle RST, Z is the centroid and RZ = 18. Find SZ."," [Triangle(R,S,T)], [IsCentroidOf(Point(Z),Triangle(R,S,T))] and [Equals(LengthOf(Line(R,Z)),18)] [Find(LengthOf(Line(S,Z)))]."
m \widehat JH = 114. Find m \angle 2.,"[Equals(MeasureOf(Arc(J,H)),114)] [Find(MeasureOf(Angle(2)))]."
Find m \angle T.,[Find(MeasureOf(Angle(T)))].
Find the exact circumference of the circle.,[Find(CircumferenceOf(Circle($)))].
"AE is a tangent. If AD = 12 and FE = 18, how long is AE to the nearest tenth unit?","[Tangent(Line(A,E),Circle($))]. If [Equals(LengthOf(Line(A,D)),12)] and [Equals(LengthOf(Line(F,E)),18)] [Find(LengthOf(Line(A,E)))] to nearest tenth unit?"
Express the ratio of \tan A as a decimal to the nearest hundredth.,[Find(RatioOf(TanOf(Angle(A))))] to nearest hundredth.
Trapezoid MNPQ has an area of 360 square feet. Find the length of MN.,"[Equals(AreaOf(Trapezoid(M,N,P,Q)),360)] [Find(LengthOf(Line(M,N)))]."
Find JN if \triangle JMN is an isosceles triangle with JM \cong MN.,"[Find(LengthOf(Line(J,N)))] if [Isosceles(Triangle(J,M,N))] with [Equals(LengthOf(Line(J,M)),Line(M,N))]."
"If QV = 8, what it the diameter of \odot Q.","If [Equals(LengthOf(Line(Q,V)),8)] [Find(DiameterOf(Circle(Q)))]."
"isosceles trapezoid TWYZ with \angle Z \cong \angle Y, m \angle Z = 30x, \angle T \cong \angle W, and m \angle T = 20x, find Z.","[Isosceles(Trapezoid(T,W,Y,Z))] with [Equals(Angle(Z),Angle(Y))], [Equals(MeasureOf(Angle(Z)),30x)] [Equals(Angle(T),Angle(W))] and [Equals(MeasureOf(Angle(T)),20x)] [Find(Angle(Z))]."
Use parallelogram ABCD to find BC.,"Use [Parallelogram(A,B,C,D)] to [Find(LengthOf(Line(B,C)))]."
Find AE.,"[Find(LengthOf(Line(A,E)))]."
The segment is tangent to the circle. Find x to the nearest hundredth.,"[Tangent(Line($),Circle($))] to [Circle($)]. [Find(x)] to nearest hundredth."
"For the pair of similar figures, use the given areas to find x.","[Similar(Shape($1),Shape($2))], to [Find(x)]."
"If J, P, and L are the midpoints of KH, HM and MK, respectively. Find z.","If [IsMidpointOf(Point(J),Line(K,H))], [IsMidpointOf(Point(P),Line(H,M))], [IsMidpointOf(Point(L),Line(M,K))],,. [Find(z)]."
H is the incenter of \triangle ABC. Find m \angle HAC.,"[IsIncenterOf(Point(H),Triangle(A,B,C))]. [Find(MeasureOf(Angle(H,A,C)))]."
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
"a = 8, b = 15, and c = 17, find \tan B.","[Equals(a,8)] [Equals(b,15)] and [Equals(c,17)] [Find(TanOf(Angle(B)))]."
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Find the perimeter of the figure.,[Find(PerimeterOf(Shape($)))].
Find z.,[Find(z)].
"Find PW, if XZ = 18 and PY = 3.","[Find(LengthOf(Line(P,W)))], if [Equals(LengthOf(Line(X,Z)),18)] and [Equals(LengthOf(Line(P,Y)),3)]."
Find x in the figure.,[Find(x)].
"In the figure, GK \cong GH and HK \cong KJ. If m \angle HGK = 28, find m \angle HJK.",", [Equals(LengthOf(Line(G,K)),Line(G,H))] and [Equals(LengthOf(Line(H,K)),Line(K,J))]. If [Equals(MeasureOf(Angle(H,G,K)),28)] [Find(MeasureOf(Angle(H,J,K)))]."
Use parallelogram NQRM to find NQ.,"Use [Parallelogram(N,Q,R,M)] to [Find(LengthOf(Line(N,Q)))]."
Find the exact circumference of the circle below.,[Find(CircumferenceOf(Circle($)))].
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find m \widehat CF.,"[Find(MeasureOf(Arc(C,F)))]."
"ABCD is a rectangle. If AC = 30-x and BD = 4x-60, find x."," [Rectangle(A,B,C,D)]. If [Equals(LengthOf(Line(A,C)),30-x)] and [Equals(LengthOf(Line(B,D)),4x-60)] [Find(x)]."
Find y.,[Find(y)].
"MC = 7, RM = 4, and AT = 16. Find RB.","[Equals(LengthOf(Line(M,C)),7)] [Equals(LengthOf(Line(R,M)),4)] and [Equals(LengthOf(Line(A,T)),16)] [Find(LengthOf(Line(R,B)))]."
Find the perimeter of the polygon for the given information. BY = CZ = AX = 2.5 diameter of \odot G = 5.,"[Find(PerimeterOf(Polygon($)))] for. [Equals(LengthOf(Line(B,Y)),2.5)] [Equals(LengthOf(Line(C,Z)),2.5)] [Equals(LengthOf(Line(A,X)),2.5)] [Equals(DiameterOf(Circle(G)),5)]."
Find x in the figure.,[Find(x)].
Find the length of \widehat ZY. Round to the nearest hundredth.,"[Find(LengthOf(Arc(Z,Y)))]. Round to nearest hundredth."
"In the figure, LH is the midsegment of trapezoid FGJK. What is the value of x?",", [IsMidsegmentOf(Line(L,H),Trapezoid(F,G,J,K))]. [Find(x)]?"
Find x.,[Find(x)].
"Segments AD and CE are medians of \triangle ACB, AD \perp CE, AB = 10, and CE = 9. Find CA.","[IsMedianOf(Line(A,D),Triangle(A,C,B))], [IsMedianOf(Line(C,E),Triangle(A,C,B))], [Perpendicular(Line(A,D),Line(C,E))], [Equals(LengthOf(Line(A,B)),10)] and [Equals(LengthOf(Line(C,E)),9)] [Find(LengthOf(Line(C,A)))]."
Find x.,[Find(x)].
"Find the area of the shaded sector. Round to the nearest tenth, if necessary.","[Find(AreaOf(Shaded(Sector($))))]. Round to nearest tenth, if necessary."
Use parallelogram ABCD to find m \angle BCF.,"Use [Parallelogram(A,B,C,D)] to [Find(MeasureOf(Angle(B,C,F)))]."
Find m \angle FED.,"[Find(MeasureOf(Angle(F,E,D)))]."
Find x.,[Find(x)].
P is the incenter of \triangle AEC. Find DE. Rounded to the nearest hundredth.,"[IsIncenterOf(Point(P),Triangle(A,E,C))]. [Find(LengthOf(Line(D,E)))]. Rounded to nearest hundredth."
Find the area of the quadrilateral.,[Find(AreaOf(Quadrilateral($)))].
Find y.,[Find(y)].
Find z.,[Find(z)].
Find x.,[Find(x)].
Find x.,[Find(x)].
Find x.,[Find(x)].
Find the measure of \angle 3 if m \angle DGF = 53 and m \angle AGC = 40.,"[Find(MeasureOf(Angle(3)))] if [Equals(MeasureOf(Angle(D,G,F)),53)] and [Equals(MeasureOf(Angle(A,G,C)),40)]."
Find x.,[Find(x)].
Find x.,[Find(x)].
Find the measure of m \angle K.,[Find(MeasureOf(Angle(K)))].
Find x.,[Find(x)].
Find y.,[Find(y)].
"Find the area of quadrilateral XYZW if XZ = 39, HW = 20, and YG = 21.","[Find(AreaOf(Quadrilateral(X,Y,Z,W)))] if [Equals(LengthOf(Line(X,Z)),39)] [Equals(LengthOf(Line(H,W)),20)] and [Equals(LengthOf(Line(Y,G)),21)]."
"In \odot X, AB = 30, CD = 30, and m \widehat CZ = 40. Find m \widehat YB.","In [Circle(X)], [Equals(LengthOf(Line(A,B)),30)] [Equals(LengthOf(Line(C,D)),30)] and [Equals(MeasureOf(Arc(C,Z)),40)] [Find(MeasureOf(Arc(Y,B)))]."
Find m \widehat WX.,"[Find(MeasureOf(Arc(W,X)))]."
Find x.,[Find(x)].
Find m \angle S.,[Find(MeasureOf(Angle(S)))].
Find x.,[Find(x)].
"In the figure, m \angle 12 = 64. Find the measure of \angle 8.",", [Equals(MeasureOf(Angle(12)),64)] [Find(MeasureOf(Angle(8)))]."
"In \triangle ABC, CD is an altitude and m \angle ACB = 90. If AD = 12 and BD = 3, find AC to the nearest tenth.","[Triangle(A,B,C)], [Equals(Line(C,D),AltitudeOf(Triangle(A,B,C)))] and [Equals(MeasureOf(Angle(A,C,B)),90)] If [Equals(LengthOf(Line(A,D)),12)] and [Equals(LengthOf(Line(B,D)),3)] [Find(LengthOf(Line(A,C)))] to nearest tenth."
"Circle W has a radius of 4 units, \odot Z has a radius of 7 units, and XY = 2. Find YZ.","[Equals(RadiusOf(Circle(W)),4)] [Equals(RadiusOf(Circle(Z)),7)] and [Equals(LengthOf(Line(X,Y)),2)] [Find(LengthOf(Line(Y,Z)))]."
Find DB.,"[Find(LengthOf(Line(D,B)))]."
Find the measure of \angle 2.,[Find(MeasureOf(Angle(2)))].
"In the figure, m \angle 12 = 64. Find the measure of \angle 13.",", [Equals(MeasureOf(Angle(12)),64)] [Find(MeasureOf(Angle(13)))]."
"In \triangle RST, Z is the centroid and RZ = 18. Find SR."," [Triangle(R,S,T)], [IsCentroidOf(Point(Z),Triangle(R,S,T))] and [Equals(LengthOf(Line(R,Z)),18)] [Find(LengthOf(Line(S,R)))]."
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
"If ABCDE \sim PQRST, find the scale factor of ABCDE to PQRST.","If [Similar(Pentagon(A,B,C,D,E),Pentagon(P,Q,R,S,T))], [Find(ScaleFactorOf(Pentagon(A,B,C,D,E),Pentagon(P,Q,R,S,T)))]."
Find x.,[Find(x)].
"In the figure, QR \parallel TS, QT \parallel RS, and m \angle 1 = 131. Find the measure of \angle 8.",", [Parallel(Line(Q,R),Line(T,S))], [Parallel(Line(Q,T),Line(R,S))] and [Equals(MeasureOf(Angle(1)),131)] [Find(MeasureOf(Angle(8)))]."
Find z.,[Find(z)].
"Find the perimeter of the given triangle. \triangle ABC, if \triangle ABC \sim \triangle CBD, CD = 4, DB = 3, and CB = 5.","[Find(PerimeterOf(Triangle($)))]. [Triangle(A,B,C)], if [Similar(Triangle(A,B,C),Triangle(C,B,D))], [Equals(LengthOf(Line(C,D)),4)] [Equals(LengthOf(Line(D,B)),3)] and [Equals(LengthOf(Line(C,B)),5)]."
Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. Round to nearest tenth if necessary. [Tangent(Line($),Circle($))]."
The two polygons are similar. Find x.,"two [Similar(Polygon($1),Polygon($2))]. [Find(x)]."
QS is a diameter of \odot V. Find m \widehat STP.,"[IsDiameterOf(Line(Q,S),Circle(V))]. [Find(MeasureOf(Arc(S,T,P)))]."
"Quadrilateral ABCD is a rectangle. If m \angle ADB = 4x+8 and m \angle DBA = 6x+12, find x."," [Rectangle(A,B,C,D)]. If [Equals(MeasureOf(Angle(A,D,B)),4x+8)] and [Equals(MeasureOf(Angle(D,B,A)),6x+12)] [Find(x)]."
Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.,"[Find(x)] to nearest tenth. [Tangent(Line($),Circle($))]."
Find QR if \triangle QRS is an equilateral triangle.,"[Find(LengthOf(Line(Q,R)))] if [Equilateral(Triangle(Q,R,S))] [Triangle($)]."
"Find the area of the figure. Round to the nearest hundredth, if necessary.","[Find(AreaOf(Shape($)))]. Round to nearest hundredth, if necessary."
"If AN is 5 meters long, find the exact circumference of \odot N.","If [Equals(Line(A,N),5)] [Find(CircumferenceOf(Circle(N)))]."
Find RS.,"[Find(LengthOf(Line(R,S)))]."
Find x. Round side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
"If WXYZ is a kite, find m \angle Z.","If [Kite(W,X,Y,Z)], [Find(MeasureOf(Angle(Z)))]."
If ABCD is a kite. Find m \angle C.,"If [Kite(A,B,C,D)]. [Find(MeasureOf(Angle(C)))]."
Find KL.,"[Find(LengthOf(Line(K,L)))]."
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
Find the area of the shaded region. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth.
Find y in the parallelogram.,[Find(y)] in [Parallelogram($)].
Find the circumference of \odot A.,[Find(CircumferenceOf(Circle(A)))].
Each pair of polygons is similar. Find AB.,"[Similar(Polygon($1),Polygon($2))]. [Find(LengthOf(Line(A,B)))]."
Find x.,[Find(x)].
"In the figure, m \angle 1 = 123. Find the measure of \angle 5.",", [Equals(MeasureOf(Angle(1)),123)] [Find(MeasureOf(Angle(5)))]."
Find m \angle R.,[Find(MeasureOf(Angle(R)))].
Find m \angle K.,[Find(MeasureOf(Angle(K)))].
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. [Regular(Polygon($))]. Round to nearest tenth.
"If AC = 12 and AB = 25, what is the measure of \angle B to the nearest tenth?","If [Equals(LengthOf(Line(A,C)),12)] and [Equals(LengthOf(Line(A,B)),25)] [Find(MeasureOf(Angle(B)))] to nearest tenth?"
"In the figure, QR \parallel TS, QT \parallel RS, and m \angle 1 = 131. Find the measure of \angle 6.",", [Parallel(Line(Q,R),Line(T,S))], [Parallel(Line(Q,T),Line(R,S))] and [Equals(MeasureOf(Angle(1)),131)] [Find(MeasureOf(Angle(6)))]."
Find BD.,"[Find(LengthOf(Line(B,D)))]."
Find \angle 10.,[Find(MeasureOf(Angle(10)))].
Find the area of \parallelogram ABCD.,"[Find(AreaOf(Parallelogram(A,B,C,D)))]."
"In the figure, m \angle 11 = 62 and m \angle 14 = 38. Find the measure of \angle 10.",", [Equals(MeasureOf(Angle(11)),62)] and [Equals(MeasureOf(Angle(14)),38)] [Find(MeasureOf(Angle(10)))]."
Find x.,[Find(x)].
"In the figure, m \angle 1 = 58, m \angle 2 = 47, and m \angle 3 = 26. Find the measure of \angle 7.",", [Equals(MeasureOf(Angle(1)),58)] [Equals(MeasureOf(Angle(2)),47)] and [Equals(MeasureOf(Angle(3)),26)] [Find(MeasureOf(Angle(7)))]."
"If QRST is a kite, find m \angle RST.","If [Kite(Q,R,S,T)], [Find(MeasureOf(Angle(R,S,T)))]."
"In \odot P, m \widehat EN = 66 and m \angle GPM = 89. Find m \angle GME.","In [Circle(P)], [Equals(MeasureOf(Arc(E,N)),66)] and [Equals(MeasureOf(Angle(G,P,M)),89)] [Find(MeasureOf(Angle(G,M,E)))]."
Find x.,[Find(x)].
The two circles are congruent. Find x.,"[Congruent(Circle($),Circle($))]. [Find(x)]."
Find x. Round the side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
What is the value of x in the figure?,[Find(x)]?
Find the variable of d to the nearest tenth. Assume that segments that appear to be tangent are tangent.,"[Find(d)] to nearest tenth. [Tangent(Line($),Circle($))]."
Find m \angle C.,[Find(MeasureOf(Angle(C)))].
Find m \angle 4.,[Find(MeasureOf(Angle(4)))].
Find \sin A.,[Find(SinOf(Angle(A)))].
"If LK = 4, MP = 3, PQ = 6, KJ = 2, RS = 6, and LP = 2, find QR.","If [Equals(LengthOf(Line(L,K)),4)] [Equals(LengthOf(Line(M,P)),3)] [Equals(LengthOf(Line(P,Q)),6)] [Equals(LengthOf(Line(K,J)),2)] [Equals(LengthOf(Line(R,S)),6)] and [Equals(LengthOf(Line(L,P)),2)] [Find(LengthOf(Line(Q,R)))]."
Find the measure of \angle DFB on \odot F with diameter AC.,"[Find(MeasureOf(Angle(D,F,B)))] on [Circle(F)], [IsDiameterOf(Line(A,C),Circle(F))]."
Find x.,[Find(x)].
"Find the area of the shaded sector. Round to the nearest tenth, if necessary.","[Find(AreaOf(Shaded(Sector($))))]. Round to nearest tenth, if necessary."
\triangle JKL \sim \triangle WYZ. Find y.,"[Similar(Triangle(J,K,L),Triangle(W,Y,Z))]. [Find(y)]."
Find x. Round the side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
"Quadrilateral MNOP is a rhombus. If PR = 12, find RN."," [Rhombus(M,N,O,P)]. If [Equals(LengthOf(Line(P,R)),12)] [Find(LengthOf(Line(R,N)))]."
Find m \angle Q.,[Find(MeasureOf(Angle(Q)))].
Find y.,[Find(y)].
ACDF \sim VWYZ. Find y.,"[Similar(Quadrilateral(A,C,D,F),Quadrilateral(V,W,Y,Z))]. [Find(y)]."
Find x.,[Find(x)].
Each triangle in the figure is a 45-45-90 triangle. Find x.,"[Equals(Triangle($),Triangle($1,$2,$3))], [Equals(MeasureOf(Angle($1)),45)], [Equals(MeasureOf(Angle($2)),45)], [Equals(MeasureOf(Angle($3)),90)]. [Find(x)]."
Find the area of the shaded region. Assume that the triangle is equilateral.,[Find(AreaOf(Shaded(Shape($))))]. Assume [Equilateral(Triangle($))].
Find AB.,"[Find(LengthOf(Line(A,B)))]."
Find x.,[Find(x)].
Find the exact circumference of the circle.,[Find(CircumferenceOf(Circle($)))].
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
"Polygon ABCD \sim polygon AEFG, m \angle AGF = 108, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26. Find DC.","[Similar(Quadrilateral(A,B,C,D),Quadrilateral(A,E,F,G))], [Equals(MeasureOf(Angle(A,G,F)),108)] [Equals(LengthOf(Line(G,F)),14)] [Equals(LengthOf(Line(A,D)),12)] [Equals(LengthOf(Line(D,G)),4.5)] [Equals(LengthOf(Line(E,F)),8)] and [Equals(LengthOf(Line(A,B)),26)] [Find(LengthOf(Line(D,C)))]."
Find m \angle 4.,[Find(MeasureOf(Angle(4)))].
Find x.,[Find(x)].
GJ is a diameter of \odot K. Find m \widehat GLH.,"[IsDiameterOf(Line(G,J),Circle(K))]. [Find(MeasureOf(Arc(G,L,H)))]."
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find the measure of \angle 4 in the figure.,[Find(MeasureOf(Angle(4)))].
Find y.,[Find(y)].
Refer to trapezoid CDFG with median HE. Let YZ be the median of HEFG. Find YZ.,"[Trapezoid(C,D,F,G)], [IsMedianOf(Line(H,E),Trapezoid(C,D,F,G))]. Let [IsMedianOf(Line(Y,Z),Quadrilateral(H,E,F,G))]. [Find(LengthOf(Line(Y,Z)))]."
Find the area of the shaded region. Assume the inscribed polygon is regular.,[Find(AreaOf(Shaded(Shape($))))]. Assume inscribed [Regular(Polygon($))].
Find y.,[Find(y)].
Solve for x.,[Find(x)].
Find x.,[Find(x)].
Find x.,[Find(x)].
Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.,"[Find(x)] to nearest tenth. [Tangent(Line($),Circle($))]."
"In \odot K, MN = 16 and m \widehat MN = 98. Find the measure of m \widehat NJ. Round to the nearest hundredth.","In [Circle(K)], [Equals(LengthOf(Line(M,N)),16)] and [Equals(MeasureOf(Arc(M,N)),98)] [Find(MeasureOf(Arc(N,J)))]. Round to nearest hundredth."
Find the area of the shaded sector. Round to the nearest tenth.,[Find(AreaOf(Shaded(Sector($))))]. Round to nearest tenth.
Find x.,[Find(x)].
Find the area of a regular hexagon with a perimeter of 72 feet.,"[Find(AreaOf(Regular(Hexagon($))))], [Equals(PerimeterOf(Regular(Hexagon($))),72)]."
Find x.,[Find(x)].
Find MP.,"[Find(LengthOf(Line(M,P)))]."
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Find x if \odot M \cong \odot N.,"[Find(x)] if [Congruent(Circle(M),Circle(N))]."
Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. [Regular(Polygon($))]. Round to nearest tenth.
"If MN \parallel PQ, use a proportion to find the value of x.","If [Parallel(Line(M,N),Line(P,Q))], to [Find(x)]."
The pair of polygons is similar. Find AB.,"[Similar(Polygon($1),Polygon($2))]. [Find(LengthOf(Line(A,B)))]."
"In \odot P, m \widehat EN = 66 and m \angle GPM = 89. Find m \angle EGN.","In [Circle(P)], [Equals(MeasureOf(Arc(E,N)),66)] and [Equals(MeasureOf(Angle(G,P,M)),89)] [Find(MeasureOf(Angle(E,G,N)))]."
Find y.,[Find(y)].
"Find x. Round to the nearest tenth, if necessary.","[Find(x)]. Round to nearest tenth, if necessary."
Find the area of the quadrilateral.,[Find(AreaOf(Quadrilateral($)))].
Find VS.,"[Find(LengthOf(Line(V,S)))]."
Find x.,[Find(x)].
Express the ratio of \tan Q as a decimal to the nearest hundredth.,[Find(RatioOf(TanOf(Angle(Q))))] to nearest hundredth.
Find x.,[Find(x)].
Find the measure of \angle T to the nearest tenth.,[Find(MeasureOf(Angle(T)))] to nearest tenth.
Use parallelogram ABCD to find x.,"Use [Parallelogram(A,B,C,D)] to [Find(x)]."
"If FK = 3x-1, KG = 4y+3, JK = 6y-2, and KH = 2x+3, find y so that the quadrilateral is a parallelogram.","If [Equals(LengthOf(Line(F,K)),3x-1)] [Equals(LengthOf(Line(K,G)),4y+3)] [Equals(LengthOf(Line(J,K)),6y-2)] and [Equals(LengthOf(Line(K,H)),2x+3)] [Find(y)] so [Parallelogram($)]"
Find the area of the quadrilateral.,[Find(AreaOf(Quadrilateral($)))].
"For trapezoid QRST, M and P are midpoints of the legs. If TS = 2x+2, QR = 5x+3, and PM = 13, find TS.","[Trapezoid(Q,R,S,T)], [IsMidpointOf(Point(M),LegOf(Trapezoid(Q,R,S,T)))], [IsMidpointOf(Point(P),LegOf(Trapezoid(Q,R,S,T)))],. If [Equals(LengthOf(Line(T,S)),2x+2)] [Equals(LengthOf(Line(Q,R)),5x+3)] and [Equals(LengthOf(Line(P,M)),13)] [Find(LengthOf(Line(T,S)))]."
Find m \angle P.,[Find(MeasureOf(Angle(P)))].
Find x.,[Find(x)].
Find x.,[Find(x)].
"If XN = t-2, NZ = t+1, XM = 2, and XY = 10, solve for t.","If [Equals(LengthOf(Line(X,N)),t-2)] [Equals(LengthOf(Line(N,Z)),t+1)] [Equals(LengthOf(Line(X,M)),2)] and [Equals(LengthOf(Line(X,Y)),10)] [Find(t)]."
Find the perimeter or circumference of the figure. Round to the nearest tenth.,[Find(PerimeterOf(Shape($)))]. Round to nearest tenth.
Find the measure of the altitude drawn to the hypotenuse.,"[Find(LengthOf(AltitudeOf(Triangle($1,$2,$3))))], [IsHypotenuseOf(Line($1,$3),Triangle($1,$2,$3))]."
Quadrilateral ABCD is a rectangle. m \angle 2 = 40. Find m \angle 7.," [Rectangle(A,B,C,D)]. [Equals(MeasureOf(Angle(2)),40)] [Find(MeasureOf(Angle(7)))]."
Find x.,[Find(x)].
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Q is the centroid and BE = 9. Find QE.,"[IsCentroidOf(Point(Q),Shape($))] and [Equals(LengthOf(Line(B,E)),9)] [Find(LengthOf(Line(Q,E)))]."
Solve for x in the figure.,[Find(x)].
"Quadrilateral ABCD is inscribed in \odot Z such that m \angle BZA = 104, m \widehat CB = 94, and AB \parallel DC. Find m \widehat ADC.","[InscribedIn(Quadrilateral(A,B,C,D),Circle(Z))] [Equals(MeasureOf(Angle(B,Z,A)),104)] [Equals(MeasureOf(Arc(C,B)),94)] and [Parallel(Line(A,B),Line(D,C))]. [Find(MeasureOf(Arc(A,D,C)))]."
Square FGHJ is inscribed in \odot K. Find the measure of a central angle.,"[InscribedIn(Square(F,G,H,J),Circle(K))]. [Find(MeasureOf(Angle($)))]."
"In rhombus LMPQ, m \angle QLM = 2x^{2}-10, m \angle QPM = 8x, and MP = 10. Find m \angle LPQ.","In [Rhombus(L,M,P,Q)], [Equals(MeasureOf(Angle(Q,L,M)),2x^{2}-10)] [Equals(MeasureOf(Angle(Q,P,M)),8x)] and [Equals(LengthOf(Line(M,P)),10)] [Find(MeasureOf(Angle(L,P,Q)))]."
Find x.,[Find(x)].
Find DX if EX = 24 and DE = 7.,"[Find(LengthOf(Line(D,X)))] if [Equals(LengthOf(Line(E,X)),24)] and [Equals(LengthOf(Line(D,E)),7)]."
Find m \angle 8.,[Find(MeasureOf(Angle(8)))].
Find m \angle 4.,[Find(MeasureOf(Angle(4)))].
Find z in the figure.,[Find(z)].
Find m \angle TQR.,"[Find(MeasureOf(Angle(T,Q,R)))]."
Use parallelogram ABCD to find y.,"Use [Parallelogram(A,B,C,D)] to [Find(y)]."
Find the measure of \angle 3.,[Find(MeasureOf(Angle(3)))].
Find x.,[Find(x)].
"Find x. Round to the nearest tenth, if necessary.","[Find(x)]. Round to nearest tenth, if necessary."
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find y.,[Find(y)].
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
Find x.,[Find(x)].
Find the area of the figure.,[Find(AreaOf(Shape($)))].
Find the measure of \angle R to the nearest tenth.,[Find(MeasureOf(Angle(R)))] to nearest tenth.
Find x.,[Find(x)].
"If \frac{IJ}{XJ} = \frac{HJ}{YJ}, m \angle WXJ = 130, and m \angle WZG = 20, find m \angle JHG.","If [Equals(RatioOf(Line(I,J),Line(X,J)),RatioOf(Line(H,J),Line(Y,J)))], [Equals(MeasureOf(Angle(W,X,J)),130)] and [Equals(MeasureOf(Angle(W,Z,G)),20)] [Find(MeasureOf(Angle(J,H,G)))]."
"m \angle 19 = 100+20x, m \angle 20 = 20x. Find the measure of \angle 20.","[Equals(MeasureOf(Angle(19)),100+20x)] [Equals(MeasureOf(Angle(20)),20x)] [Find(MeasureOf(Angle(20)))]."
Find y.,[Find(y)].
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find the perimeter of the triangle. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Triangle($)))]. Round to nearest tenth if necessary.
"If c = 8, find a.","If [Equals(c,8)] [Find(a)]."
"In the figure at the right, what is the value of p in terms of m and n?",", [Find(p)] ?"
"If MNPQ \sim XYZW, find the scale factor of MNPQ to XYZW.","If [Similar(Quadrilateral(M,N,P,Q),Quadrilateral(X,Y,Z,W))], [Find(ScaleFactorOf(Quadrilateral(M,N,P,Q),Quadrilateral(X,Y,Z,W)))]."
"BC \parallel DF. AB = x+5, BD = 12, AC = 3x+1, and CF = 15. Find x.","[Parallel(Line(B,C),Line(D,F))]. [Equals(LengthOf(Line(A,B)),x+5)] [Equals(LengthOf(Line(B,D)),12)] [Equals(LengthOf(Line(A,C)),3x+1)] and [Equals(LengthOf(Line(C,F)),15)] [Find(x)]."
Find y.,[Find(y)].
HK and IG are diameters of \odot L. Find m \widehat HI.,"[IsDiameterOf(Line(H,K),Circle(L))], [IsDiameterOf(Line(I,G),Circle(L))]. [Find(MeasureOf(Arc(H,I)))]."
Find x.,[Find(x)].
Use the Pythagorean Theorem to find the length of the hypotenuse of the right triangle.,[UseTheorem(Pythagorean_Theorem)] to [Find(LengthOf(HypotenuseOf(Right(Triangle($)))))].
Find the area of the figure.,[Find(AreaOf(Shape($)))].
A square with 5-centimeter sides is inscribed in a circle. What is the circumference of the circle? Round your answer to the nearest tenth of a centimeter.,"[Equals(SideOf(Square($)),5)] [InscribedIn(Square($),Circle($))]. [Find(CircumferenceOf(Circle($)))]? Round to nearest tenth of centimeter."
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
"If m \angle ZXW = x-11 and m \angle WZX = x-9, find m \angle ZXY.","If [Equals(MeasureOf(Angle(Z,X,W)),x-11)] and [Equals(MeasureOf(Angle(W,Z,X)),x-9)] [Find(MeasureOf(Angle(Z,X,Y)))]."
"If PR \parallel KL, KN = 9, LN = 16, PM = 2 KP, find KP.","If [Parallel(Line(P,R),Line(K,L))], [Equals(LengthOf(Line(K,N)),9)] [Equals(LengthOf(Line(L,N)),16)] [Equals(LengthOf(Line(P,M)),Mul(Line(K,P),2))], [Find(LengthOf(Line(K,P)))]."
Find x.,[Find(x)].
Find the value of x in the diagram.,[Find(x)].
Find x.,[Find(x)].
Find XY.,"[Find(LengthOf(Line(X,Y)))]."
Find z.,[Find(z)].
Find z in the figure.,[Find(z)].
Polygons FGHJK and VWXUZ are similar regular pentagons. Find the scale factor.,"[Similar(Pentagon(F,G,H,J,K),Pentagon(V,W,X,U,Z))] regular pentagons. [Find(ScaleFactorOf(Shape($1),Shape($2)))]."
What is the value of x in the figure below? Round to the nearest tenth.,[Find(x)]? Round to nearest tenth.
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
"m \angle 11 = 4x, m \angle 12 = 2x-6. Find the measure of \angle 12.","[Equals(MeasureOf(Angle(11)),4x)] [Equals(MeasureOf(Angle(12)),2x-6)] [Find(MeasureOf(Angle(12)))]."
"The area of trapezoid JKLM is 138 square feet. The area of trapezoid QRST is 5.52 square feet. If trapezoid JKLM \sim trapezoid QRST, find the scale factor from trapezoid JKLM to trapezoid QRST.","[Equals(AreaOf(Trapezoid(J,K,L,M)),138)] [Equals(AreaOf(Trapezoid(Q,R,S,T)),5.52)] If [Similar(Trapezoid(J,K,L,M),Trapezoid(Q,R,S,T))], [Find(ScaleFactorOf(Trapezoid(J,K,L,M),Trapezoid(Q,R,S,T)))]."
\triangle RST \cong \triangle VUT. What is the area of \triangle RST?,"[Congruent(Triangle(R,S,T),Triangle(V,U,T))]. [Find(AreaOf(Triangle(R,S,T)))]?"
Find the perimeter of the parallelogram.,[Find(PerimeterOf(Parallelogram($)))].
Each pair of polygons is similar. Find y.,"[Similar(Polygon($1),Polygon($2))]. [Find(y)]."
Find y.,[Find(y)].
\triangle RST is a right triangle. Find m \angle R.,"[Right(Triangle(R,S,T))]. [Find(MeasureOf(Angle(R)))]."
Find the measure of \angle 1 in the figure.,[Find(MeasureOf(Angle(1)))].
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find the measure of \angle C.,[Find(MeasureOf(Angle(C)))].
"\triangle DFG and \triangle FGH are isosceles, m \angle FDH = 28 and DG \cong FG \cong FH. Find the measure of \angle DFG.","[Isosceles(Triangle(D,F,G))], [Isosceles(Triangle(F,G,H))], [Equals(MeasureOf(Angle(F,D,H)),28)] and [Equals(LengthOf(Line(D,G)),Line(F,G))], [Equals(LengthOf(Line(F,G)),Line(F,H))]. [Find(MeasureOf(Angle(D,F,G)))]."
Find x. Round the side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
P is the incenter of \angle XYZ. Find PK.,"[IsIncenterOf(Point(P),Angle(X,Y,Z))]. [Find(LengthOf(Line(P,K)))]."
Find m \angle D.,[Find(MeasureOf(Angle(D)))].
"in \triangle XYZ, P is the centroid, KP = 3, and XJ = 8. Find XK.","in  [Triangle(X,Y,Z)], [IsCentroidOf(Point(P),Triangle(X,Y,Z))], [Equals(LengthOf(Line(K,P)),3)] and [Equals(LengthOf(Line(X,J)),8)] [Find(LengthOf(Line(X,K)))]."
Find x. Round the angle measure to the nearest degree.,[Find(x)]. Round angle measure to nearest degree.
"Find the perimeter of the figure. Round to the nearest hundredth, if necessary.","[Find(PerimeterOf(Shape($)))]. Round to nearest hundredth, if necessary."
Find x. Assume that any segment that appears to be tangent is tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find x.,[Find(x)].
Find x.,[Find(x)].
Line l is parallel to line m. What is the value of x?,"[Parallel(Line(l),Line(m))]. [Find(x)]?"
Find the area of the quadrilateral.,[Find(AreaOf(Quadrilateral($)))].
"Find ED if AE = 3, AB = 2, BC = 6, and ED = 2x-3.","[Find(LengthOf(Line(E,D)))] if [Equals(LengthOf(Line(A,E)),3)] [Equals(LengthOf(Line(A,B)),2)] [Equals(LengthOf(Line(B,C)),6)] and [Equals(LengthOf(Line(E,D)),2x-3)]."
Find m \angle Z.,[Find(MeasureOf(Angle(Z)))].
Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. Round to nearest tenth if necessary. [Tangent(Line($),Circle($))]."
Find the perimeter or circumference of the figure. Round to the nearest tenth.,[Find(PerimeterOf(Shape($)))]. Round to nearest tenth.
Find m \angle H.,[Find(MeasureOf(Angle(H)))].
Find x.,[Find(x)].
Find y. Assume that segments that appear to be tangent are tangent. Round to the nearest tenth if necessary.,"[Find(y)]. [Tangent(Line($),Circle($))]. Round to nearest tenth if necessary."
Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. [Regular(Polygon($))]. Round to nearest tenth.
"In \odot R, SU = 20, YW = 20, and m \widehat YX = 45. Find m \widehat YW.","In [Circle(R)], [Equals(LengthOf(Line(S,U)),20)] [Equals(LengthOf(Line(Y,W)),20)] and [Equals(MeasureOf(Arc(Y,X)),45)] [Find(MeasureOf(Arc(Y,W)))]."
Find the area of the blue sector.,[Find(AreaOf(Blue(Sector($))))].
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Find the measure of the altitude drawn to the hypotenuse.,"[Find(LengthOf(AltitudeOf(Triangle($1,$2,$3))))], [IsHypotenuseOf(Line($1,$3),Triangle($1,$2,$3))]."
Find x.,[Find(x)].
Find the area of the shaded sector. Round to the nearest tenth.,[Find(AreaOf(Shaded(Sector($))))]. Round to nearest tenth.
"In right triangle ABC shown below, what is the measure of \angle A to the nearest tenth of a degree?","In [Right(Triangle(A,B,C))], [Find(MeasureOf(Angle(A)))] to nearest tenth of degree?"
Find x. Round side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
"In the figure, m \angle 1 = 123. Find the measure of \angle 11.",", [Equals(MeasureOf(Angle(1)),123)] [Find(MeasureOf(Angle(11)))]."
"If TP = 4x+2, QP = 2y-6, PS = 5y-12, and PR = 6x-4, find x so that the quadrilateral is a parallelogram.","If [Equals(LengthOf(Line(T,P)),4x+2)] [Equals(LengthOf(Line(Q,P)),2y-6)] [Equals(LengthOf(Line(P,S)),5y-12)] and [Equals(LengthOf(Line(P,R)),6x-4)] [Find(x)] so [Parallelogram($)]"
Find the area of the shaded region. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth.
Find x.,[Find(x)].
Find x.,[Find(x)].
Use parallelogram to find b.,Use [Parallelogram($)] to [Find(b)].
Find y.,[Find(y)].
\triangle RST \cong \triangle XYZ. Find x.,"[Congruent(Triangle(R,S,T),Triangle(X,Y,Z))]. [Find(x)]."
Find a.,[Find(a)].
Find the area of the figure.,[Find(AreaOf(Shape($)))].
"Use parallelogram to, find y.",Use [Parallelogram($)] to [Find(y)].
Find x.,[Find(x)].
Quadrilateral EFGH is a rectangle. Find m \angle HEF+m \angle EFG.," [Rectangle(E,F,G,H)]. [Find(Add(MeasureOf(Angle(H,E,F)),MeasureOf(Angle(E,F,G))))]."
"Use rectangle LMNP, parallelogram LKMJ to solve the problem. If m \angle PLK = 110, find m \angle LKM.","Use [Rectangle(L,M,N,P)], [Parallelogram(L,K,M,J)] to. If [Equals(MeasureOf(Angle(P,L,K)),110)] [Find(MeasureOf(Angle(L,K,M)))]."
Find TR.,"[Find(LengthOf(Line(T,R)))]."
Find x.,[Find(x)].
Find x if AD is an altitude of \triangle ABC.,"[Find(x)] if [Equals(Line(A,D),AltitudeOf(Triangle(A,B,C)))]."
"In A, the radius is 14 and CD = 22. Find EB. Round to the nearest hundredth."," [Circle(A)], [Equals(RadiusOf(Circle(A)),14)] and [Equals(LengthOf(Line(C,D)),22)] [Find(LengthOf(Line(E,B)))]. Round to nearest hundredth."
Refer to the figure at the right. Find the value of m \angle ABD if p \parallel q.,"[Shape($)]. [Find(MeasureOf(Angle(A,B,D)))] if [Parallel(Line(p),Line(q))]."
Trapezoid NOPQ has an area of 250 square inches. Find the height of NOPQ.,"[Equals(AreaOf(Trapezoid(N,O,P,Q)),250)] [Find(HeightOf(Quadrilateral(N,O,P,Q)))]."
Refer to the figure at the right. Find the value of x if p \parallel q.,"[Shape($)]. [Find(x)] if [Parallel(Line(p),Line(q))]."
Find x in the figure.,[Find(x)].
"In rectangle JKLM shown below, JL and MK are diagonals. If JL = 2x+5 and KM = 4x-11, what is x?","[Rectangle(J,K,L,M)], [IsDiagonalOf(Line(J,L),Rectangle(J,K,L,M))], [IsDiagonalOf(Line(M,K),Rectangle(J,K,L,M))]. If [Equals(LengthOf(Line(J,L)),2x+5)] and [Equals(LengthOf(Line(K,M)),4x-11)] [Find(x)]?"
"In \triangle ABC, BD is a median. If AD = 3x+5 and CD = 5x-1, find AC.","[Triangle(A,B,C)], [IsMedianOf(Line(B,D),Triangle(A,B,C))]. If [Equals(LengthOf(Line(A,D)),3x+5)] and [Equals(LengthOf(Line(C,D)),5x-1)] [Find(LengthOf(Line(A,C)))]."
Find the value of the variable x in the figure.,[Find(x)].
Find LN.,"[Find(LengthOf(Line(L,N)))]."
"Lines l, m, and n are perpendicular bisectors of \triangle PQR and meet at T. If TQ = 2x, PT = 3y-1, and TR = 8, find y.","[IsPerpendicularBisectorOf(Line(l),Triangle(P,Q,R))], [IsPerpendicularBisectorOf(Line(m),Triangle(P,Q,R))], [IsPerpendicularBisectorOf(Line(n),Triangle(P,Q,R))]. [IntersectAt(Line(l),Line(m),Line(n),Point(T))]. If [Equals(LengthOf(Line(T,Q)),2x)] [Equals(LengthOf(Line(P,T)),3y-1)] and [Equals(LengthOf(Line(T,R)),8)] [Find(y)]."
Quadrilateral ABCD is a rectangle. m \angle 2 = 40. Find m \angle 6.," [Rectangle(A,B,C,D)]. [Equals(MeasureOf(Angle(2)),40)] [Find(MeasureOf(Angle(6)))]."
"If \angle RST is a right angle, SU \perp RT, UV \perp ST, and m \angle RTS = 47, find m \angle SUV.","If [RightAngle(Angle(R,S,T))], [Perpendicular(Line(S,U),Line(R,T))], [Perpendicular(Line(U,V),Line(S,T))] and [Equals(MeasureOf(Angle(R,T,S)),47)] [Find(MeasureOf(Angle(S,U,V)))]."
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
\triangle PQS \cong \triangle RQS. Find y.,"[Congruent(Triangle(P,Q,S),Triangle(R,Q,S))]. [Find(y)]."
Find x.,[Find(x)].
Find x so that m \parallel n.,"[Find(x)] so [Parallel(Line(m),Line(n))]."
Find SR.,"[Find(LengthOf(Line(S,R)))]."
Triangle WXY has an area of 248 square inches. Find the length of the base.,"[Equals(AreaOf(Triangle(W,X,Y)),248)] [Find(LengthOf(BaseOf(Polygon($))))]."
Find x.,[Find(x)].
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Find m \angle C.,[Find(MeasureOf(Angle(C)))].
Find x. Round the side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
"In \odot B, m \angle LBM = 3x and m \angle LBQ = 4x+61. What is the measure of \angle PBQ?","In [Circle(B)], [Equals(MeasureOf(Angle(L,B,M)),3x)] and [Equals(MeasureOf(Angle(L,B,Q)),4x+61)] [Find(MeasureOf(Angle(P,B,Q)))]?"
Find x. Round to the nearest degree.,[Find(x)]. Round to nearest degree.
Find x. Round side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
"Find the measure of RT of equilateral triangle RST if RS = x+9, ST = 2x, and RT = 3x-9.","[Find(LengthOf(Line(R,T)))] of [Equilateral(Triangle(R,S,T))] if [Equals(LengthOf(Line(R,S)),x+9)] [Equals(LengthOf(Line(S,T)),2x)] and [Equals(LengthOf(Line(R,T)),3x-9)]."
Find x.,[Find(x)].
What is the perimeter of the triangle?,[Find(PerimeterOf(Triangle($)))]?
"Find the perimeter of \triangle CBH, if \triangle CBH \sim \triangle FEH, ADEG is a parallelogram, CH = 7, FH = 10, FE = 11, and EH = 6.","[Find(PerimeterOf(Triangle(C,B,H)))], if [Similar(Triangle(C,B,H),Triangle(F,E,H))], [Parallelogram(A,D,E,G)], [Equals(LengthOf(Line(C,H)),7)] [Equals(LengthOf(Line(F,H)),10)] [Equals(LengthOf(Line(F,E)),11)] and [Equals(LengthOf(Line(E,H)),6)]."
Find x.,[Find(x)].
"In the right triangle, what is AB if BC = 6?","In [Right(Triangle($))], [Find(LengthOf(Line(A,B)))] if [Equals(LengthOf(Line(B,C)),6)]?"
Find x.,[Find(x)].
"Find CD if AE = 8, ED = 4, and BE = 6.","[Find(LengthOf(Line(C,D)))] if [Equals(LengthOf(Line(A,E)),8)] [Equals(LengthOf(Line(E,D)),4)] and [Equals(LengthOf(Line(B,E)),6)]."
Find AF.,"[Find(LengthOf(Line(A,F)))]."
Find x.,[Find(x)].
Find \angle B of quadrilateral ABCD.,"[Find(MeasureOf(Angle(B)))] of [Quadrilateral(A,B,C,D)]."
"In \triangle PQR, ZQ = 3a-11, ZP = a+5, PY = 2c-1, YR = 4c-11, m \angle PRZ = 4b-17, m \angle ZRQ = 3b-4, m \angle QYR = 7b+6, and m \angle PXR = 2a+10. PX is an altitude of \triangle PQR. Find a.","In [Triangle(P,Q,R)], [Equals(LengthOf(Line(Z,Q)),3a-11)] [Equals(LengthOf(Line(Z,P)),a+5)] [Equals(LengthOf(Line(P,Y)),2c-1)] [Equals(LengthOf(Line(Y,R)),4c-11)] [Equals(MeasureOf(Angle(P,R,Z)),4b-17)] [Equals(MeasureOf(Angle(Z,R,Q)),3b-4)] [Equals(MeasureOf(Angle(Q,Y,R)),7b+6)] and [Equals(MeasureOf(Angle(P,X,R)),2a+10)] [Equals(Line(P,X),AltitudeOf(Triangle(P,Q,R)))]. [Find(a)]."
Find the measure of \angle 7.,[Find(MeasureOf(Angle(7)))].
Find AB.,"[Find(LengthOf(Line(A,B)))]."
JKLM is a rhombus. If CK = 8 and JK = 10. Find JC.," [Rhombus(J,K,L,M)]. If [Equals(LengthOf(Line(C,K)),8)] and [Equals(LengthOf(Line(J,K)),10)] [Find(LengthOf(Line(J,C)))]."
Find JK.,"[Find(LengthOf(Line(J,K)))]."
"In the figure, m \angle 4 = 104, m \angle 14 = 118. Find the measure of \angle 7.",", [Equals(MeasureOf(Angle(4)),104)] [Equals(MeasureOf(Angle(14)),118)] [Find(MeasureOf(Angle(7)))]."
Find the area of the shaded region.,[Find(AreaOf(Shaded(Shape($))))].
Find x.,[Find(x)].
Refer to the figure at the right. Find z.,[Shape($)]. [Find(z)].
Find x in \triangle PQR.,"[Find(x)] in [Triangle(P,Q,R)]."
"Use rhombus XYZW with m \angle WYZ = 53, VW = 3, XV = 2a-2, and ZV = \frac{5a+1}{4}. Find m \angle XYW.","Use [Rhombus(X,Y,Z,W)] with [Equals(MeasureOf(Angle(W,Y,Z)),53)] [Equals(LengthOf(Line(V,W)),3)] [Equals(LengthOf(Line(X,V)),2a-2)] and [Equals(LengthOf(Line(Z,V)),\frac{5a+1}{4})] [Find(MeasureOf(Angle(X,Y,W)))]."
"If MS is a median of \triangle MNQ, QS = 3a-14, SN = 2a+1, and m \angle MSQ = 7a+1, find the value of a.","If [IsMedianOf(Line(M,S),Triangle(M,N,Q))], [Equals(LengthOf(Line(Q,S)),3a-14)] [Equals(LengthOf(Line(S,N)),2a+1)] and [Equals(MeasureOf(Angle(M,S,Q)),7a+1)] [Find(a)]."
PM is a diameter of \odot R. Find m \widehat MNQ.,"[IsDiameterOf(Line(P,M),Circle(R))]. [Find(MeasureOf(Arc(M,N,Q)))]."
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
Find y.,[Find(y)].
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
Find m \angle D.,[Find(MeasureOf(Angle(D)))].
AD and CG are diameters of \odot B. Find m \widehat CD.,"[IsDiameterOf(Line(A,D),Circle(B))], [IsDiameterOf(Line(C,G),Circle(B))]. [Find(MeasureOf(Arc(C,D)))]."
Find b.,[Find(b)].
"In \triangle JLP, m \angle JMP = 3x-6, JK = 3y-2, and LK = 5y-8. Find LK if PK is a median.","In [Triangle(J,L,P)], [Equals(MeasureOf(Angle(J,M,P)),3x-6)] [Equals(LengthOf(Line(J,K)),3y-2)] and [Equals(LengthOf(Line(L,K)),5y-8)] [Find(LengthOf(Line(L,K)))] if [IsMedianOf(Line(P,K),Shape($))]."
The triangle is inscribed into the circle. Find the exact circumference of the circle.,"[InscribedIn(Triangle($),Circle($))]. [Find(CircumferenceOf(Circle($)))]."
Find MN if \triangle JMN is an isosceles triangle with JM \cong MN.,"[Find(LengthOf(Line(M,N)))] if [Isosceles(Triangle(J,M,N))] with [Equals(LengthOf(Line(J,M)),Line(M,N))]."
Find x.,[Find(x)].
"For the pair of similar figures, find the area of the green figure.","[Similar(Shape($1),Shape($2))], [Find(AreaOf(Green(Shape($))))]."
Find x.,[Find(x)].
Find the length of WY.,"[Find(LengthOf(Line(W,Y)))]."
"In the figure, \triangle ABC is isosceles, \triangle DCE is equilateral, and \triangle FCG is isosceles. Find the measure of the \angle 4 at vertex C.",", [Isosceles(Triangle(A,B,C))], [Equilateral(Triangle(D,C,E))] and [Isosceles(Triangle(F,C,G))]. [Find(MeasureOf(Angle(4)))], [Equals(Angle(4),Angle(C))]."
m \widehat GH = 78. Find m \angle 1.,"[Equals(MeasureOf(Arc(G,H)),78)] [Find(MeasureOf(Angle(1)))]."
"If WP is a perpendicular bisector, m \angle WHA = 8q+17, m \angle HWP = 10+q, AP = 6r+4, and PH = 22+3r, find r.","If [IsPerpendicularBisectorOf(Line(W,P),Line($))], [Equals(MeasureOf(Angle(W,H,A)),8q+17)] [Equals(MeasureOf(Angle(H,W,P)),10+q)] [Equals(LengthOf(Line(A,P)),6r+4)] and [Equals(LengthOf(Line(P,H)),22+3r)] [Find(r)]."
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
Each pair of polygons is similar. Find y.,"[Similar(Polygon($1),Polygon($2))]. [Find(y)]."
"P is the centroid of triangle QUS. If QP = 14 centimeters, what is the length of QT?","[IsCentroidOf(Point(P),Triangle(Q,U,S))]. If [Equals(LengthOf(Line(Q,P)),14)] [Find(LengthOf(Line(Q,T)))]?"
Find y.,[Find(y)].
Find WZ.,"[Find(LengthOf(Line(W,Z)))]."
The segment is tangent to the circle. Find the value of x.,"[Tangent(Line($),Circle($))] to [Circle($)]. [Find(x)]."
Find y.,[Find(y)].
The segment is tangent to the circle. Find x.,"[Tangent(Line($),Circle($))] to [Circle($)]. [Find(x)]."
"Find x if MS is an altitude of \triangle MNQ, m \angle 1 = 3x+11, and m \angle 2 = 7x+9.","[Find(x)] if [Equals(Line(M,S),AltitudeOf(Triangle(M,N,Q)))], [Equals(MeasureOf(Angle(1)),3x+11)] and [Equals(MeasureOf(Angle(2)),7x+9)]."
Find the area of the figure. Round to the nearest tenth.,[Find(AreaOf(Shape($)))]. Round to nearest tenth.
Find m \angle 7.,[Find(MeasureOf(Angle(7)))].
Find x.,[Find(x)].
"If EC is an altitude of \triangle AED, m \angle 1 = 2x+7, and m \angle 2 = 3x+13, find m \angle 1.","If [Equals(Line(E,C),AltitudeOf(Triangle(A,E,D)))], [Equals(MeasureOf(Angle(1)),2x+7)] and [Equals(MeasureOf(Angle(2)),3x+13)] [Find(MeasureOf(Angle(1)))]."
Express the ratio of \cos C as a decimal to the nearest hundredth.,[Find(RatioOf(CosOf(Angle(C))))] to nearest hundredth.
Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. [Regular(Polygon($))]. Round to nearest tenth.
Find the area of the regular polygon. Round to the nearest tenth.,[Find(AreaOf(Regular(Polygon($))))]. Round to nearest tenth.
"In the figure, m \angle 3 = 43. Find the measure of \angle 16.",", [Equals(MeasureOf(Angle(3)),43)] [Find(MeasureOf(Angle(16)))]."
Solve for x in the figure below.,[Find(x)].
Find the variable of x to the nearest tenth. Assume that segments that appear to be tangent are tangent.,"[Find(x)] to nearest tenth. [Tangent(Line($),Circle($))]."
"Triangles FGH and FHJ are inscribed in \odot K with \widehat FG \cong \widehat FI. Find x if m \angle 1 = 6x-5, and m \angle 2 = 7x+4.","[InscribedIn(Triangle(F,G,H),Circle(K))], [InscribedIn(Triangle(F,H,J),Circle(K))] with [Congruent(Arc(F,G),Arc(F,I))]. [Find(x)] if [Equals(MeasureOf(Angle(1)),6x-5)] and [Equals(MeasureOf(Angle(2)),7x+4)]."
"If BE \cong ED and m \widehat ED = 120, find m \widehat BE.","If [Equals(LengthOf(Line(B,E)),Line(E,D))] and [Equals(MeasureOf(Arc(E,D)),120)] [Find(MeasureOf(Arc(B,E)))]."
Find the area of the shaded region. Round to the nearest tenth if necessary.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth if necessary.
AB is tangent to the circle. Find x. Round to the nearest tenth.,"[Tangent(Line(A,B),Circle($))]. [Find(x)]. Round to nearest tenth."
"Find x so that GJ \parallel FK. HJ = x-5, JK = 15, FG = 18, HG = x-4.","[Find(x)] so [Parallel(Line(G,J),Line(F,K))]. [Equals(LengthOf(Line(H,J)),x-5)] [Equals(LengthOf(Line(J,K)),15)] [Equals(LengthOf(Line(F,G)),18)] [Equals(LengthOf(Line(H,G)),x-4)]."
Find the perimeter or circumference of the figure. Round to the nearest tenth.,[Find(PerimeterOf(Shape($)))]. Round to nearest tenth.
Find y.,[Find(y)].
Find x.,[Find(x)].
Find the area of \triangle JKM.,"[Find(AreaOf(Triangle(J,K,M)))]."
Find the area of the regular polygon. Round to the nearest tenth.,[Find(AreaOf(Regular(Polygon($))))]. Round to nearest tenth.
Find y.,[Find(y)].
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
"For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure.","[Similar(Shape($1),Shape($2))], to [Find(ScaleFactorOf(Blue(Shape($)),Green(Shape($))))]."
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Find x.,[Find(x)].
Find the area of the triangle. Round to the nearest hundredth.,[Find(AreaOf(Triangle($)))]. Round to nearest hundredth.
Equilateral pentagon PQRST is inscribed in \odot U. Find m \angle PQR.,"[InscribedIn(Equilateral(Pentagon(P,Q,R,S,T)),Circle(U))]. [Find(MeasureOf(Angle(P,Q,R)))]."
Find x so that m \parallel n.,"[Find(x)] so [Parallel(Line(m),Line(n))]."
Quadrilateral ABCD is shown. AC is 40 and BD is \frac{3}{5} AC. BD bisects AC. For what value of x is ABCD a parallelogram.,"[Quadrilateral(A,B,C,D)] is. [Equals(Line(A,C),40)] and [Equals(Line(B,D),Mul(Line(A,C),\frac{3}{5}))]. [BisectsAngle(Line(B,D),Line(A,C))]. [Parallelogram(A,B,C,D)], [Find(x)]."
"Use rhombus XYZW with m \angle WYZ = 53, VW = 3, XV = 2a-2, and ZV = \frac{5a+1}{4}. Find XW.","Use [Rhombus(X,Y,Z,W)] with [Equals(MeasureOf(Angle(W,Y,Z)),53)] [Equals(LengthOf(Line(V,W)),3)] [Equals(LengthOf(Line(X,V)),2a-2)] and [Equals(LengthOf(Line(Z,V)),\frac{5a+1}{4})] [Find(LengthOf(Line(X,W)))]."
"In \odot X, AB = 30, CD = 30, and m \widehat CZ = 40. Find MB.","In [Circle(X)], [Equals(LengthOf(Line(A,B)),30)] [Equals(LengthOf(Line(C,D)),30)] and [Equals(MeasureOf(Arc(C,Z)),40)] [Find(LengthOf(Line(M,B)))]."
Find x.,[Find(x)].
Find the area of the kite.,[Find(AreaOf(Kite($)))].
"If \triangle SRY \sim \triangle WXQ, RT is an altitude of \triangle SRY, XV is an altitude of \triangle WXQ, RT = 5, RQ = 4, QY = 6, and YX = 2, find XV.","If [Similar(Triangle(S,R,Y),Triangle(W,X,Q))], [Equals(Line(R,T),AltitudeOf(Triangle(S,R,Y)))], [Equals(Line(X,V),AltitudeOf(Triangle(W,X,Q)))], [Equals(LengthOf(Line(R,T)),5)] [Equals(LengthOf(Line(R,Q)),4)] [Equals(LengthOf(Line(Q,Y)),6)] and [Equals(LengthOf(Line(Y,X)),2)] [Find(LengthOf(Line(X,V)))]."
Find m \angle D.,[Find(MeasureOf(Angle(D)))].
Find m \widehat BCA.,"[Find(MeasureOf(Arc(B,C,A)))]."
The height of a triangle is 5 centimeters more than its base. The area of the triangle is 52 square centimeters. Find the height.,"[Equals(HeightOf(Triangle($)),Add(BaseOf(Polygon($)),5))]. [Equals(AreaOf(Triangle($)),52)] [Find(HeightOf(Polygon($)))]."
Find the value of the variable w.,[Find(w)].
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
Find the measure of the altitude drawn to the hypotenuse.,"[Find(LengthOf(AltitudeOf(Triangle($1,$2,$3))))], [IsHypotenuseOf(Line($1,$3),Triangle($1,$2,$3))]."
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
"In \odot O, EC and AB are diameters, and \angle BOD \cong \angle DOE \cong \angle EOF \cong \angle FOA. Find m \widehat CBF.","[Circle(O)], [IsDiameterOf(Line(E,C),Circle(O))], [IsDiameterOf(Line(A,B),Circle(O))] and [Equals(Angle(B,O,D),Angle(D,O,E))], [Equals(Angle(D,O,E),Angle(E,O,F))], [Equals(Angle(E,O,F),Angle(F,O,A))]. [Find(MeasureOf(Arc(C,B,F)))]."
"For trapezoid JKLM, A and B are midpoints of the legs. If AB = 57 and KL = 21, find JM.","[Trapezoid(J,K,L,M)], [IsMidpointOf(Point(A),LegOf(Trapezoid(J,K,L,M)))], [IsMidpointOf(Point(B),LegOf(Trapezoid(J,K,L,M)))],. If [Equals(LengthOf(Line(A,B)),57)] and [Equals(LengthOf(Line(K,L)),21)] [Find(LengthOf(Line(J,M)))]."
Find x.,[Find(x)].
Find the measure of \angle A to the nearest tenth.,[Find(MeasureOf(Angle(A)))] to nearest tenth.
Find the perimeter of the figure.,[Find(PerimeterOf(Shape($)))].
"In the figure, the vertices of quadrilateral ABCD intersect square EFGH and divide its sides into segments with measure that have a ratio of 1:2. Find the ratio between the areas of ABCD and EFGH.",", vertices of [Quadrilateral(A,B,C,D)] intersect [Square(E,F,G,H)] and divide sides into segments with measure have a ratio of 1:2. Find ratio between areas of [Quadrilateral(A,B,C,D)] and [Quadrilateral(E,F,G,H)]."
Find the area of the regular polygon. Round to the nearest tenth.,[Find(AreaOf(Regular(Polygon($))))]. Round to nearest tenth.
Find the measure of \angle D.,[Find(MeasureOf(Angle(D)))].
XY and XZ are midsegments of \triangle RST. Find m \angle RYX.,"[IsMidsegmentOf(Line(X,Y),Triangle(R,S,T))], [IsMidsegmentOf(Line(X,Z),Triangle(R,S,T))]. [Find(MeasureOf(Angle(R,Y,X)))]."
"In the figure, m \angle 11 = 62 and m \angle 14 = 38. Find the measure of \angle 8.",", [Equals(MeasureOf(Angle(11)),62)] and [Equals(MeasureOf(Angle(14)),38)] [Find(MeasureOf(Angle(8)))]."
Use parallelogram PQRS to find QR.,"Use [Parallelogram(P,Q,R,S)] to [Find(LengthOf(Line(Q,R)))]."
Find y.,[Find(y)].
"In \odot P, the diameter is 9, find the length of \widehat QT. Round to the nearest hundredth."," [Circle(P)], [Equals(DiameterOf(Circle(P)),9)] [Find(LengthOf(Arc(Q,T)))]. Round to nearest hundredth."
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find QR.,"[Find(LengthOf(Line(Q,R)))]."
"Quadrilateral ABCD is a rhombus. If m \angle BCD = 64, find m \angle BAC."," [Rhombus(A,B,C,D)]. If [Equals(MeasureOf(Angle(B,C,D)),64)] [Find(MeasureOf(Angle(B,A,C)))]."
Find m \angle K.,[Find(MeasureOf(Angle(K)))].
"Quadrilateral MNOP is a rhombus. If m \angle PON = 124, find m \angle POM."," [Rhombus(M,N,O,P)]. If [Equals(MeasureOf(Angle(P,O,N)),124)] [Find(MeasureOf(Angle(P,O,M)))]."
"Points S, T, and U are the midpoints of DE, EF, and DF, respectively. Find y.","[IsMidpointOf(Point(S),Line(D,E))], [IsMidpointOf(Point(T),Line(E,F))], [IsMidpointOf(Point(U),Line(D,F))],,. [Find(y)]."
Find y.,[Find(y)].
Each pair of polygons is similar. Find x.,"[Similar(Polygon($1),Polygon($2))]. [Find(x)]."
Find x.,[Find(x)].
Find x.,[Find(x)].
"In \odot X, AB = 30, CD = 30, and m \widehat CZ = 40. Find AM.","In [Circle(X)], [Equals(LengthOf(Line(A,B)),30)] [Equals(LengthOf(Line(C,D)),30)] and [Equals(MeasureOf(Arc(C,Z)),40)] [Find(LengthOf(Line(A,M)))]."
The segment is tangent to the circle. Find x.,"[Tangent(Line($),Circle($))] to [Circle($)]. [Find(x)]."
Triangle ABC is similar to triangle DEF. Find the scale factor.,"[Similar(Triangle(A,B,C),Triangle(D,E,F))]. [Find(ScaleFactorOf(Shape($1),Shape($2)))]."
"In \odot B, the diameter is 20 units long, and m \angle ACE = 45. Find x."," [Circle(B)], [Equals(DiameterOf(Circle(B)),20)] and [Equals(MeasureOf(Angle(A,C,E)),45)] [Find(x)]."
Find x.,[Find(x)].
m \widehat GH = 78. Find m \angle 3.,"[Equals(MeasureOf(Arc(G,H)),78)] [Find(MeasureOf(Angle(3)))]."
"If KLMN is a parallelogram, fnd x.","If [Parallelogram(K,L,M,N)], fnd x."
"Quadrilateral DEFG is a rectangle. If DF = 2(x+5)-7 and EG = 3(x-2), find EG."," [Rectangle(D,E,F,G)]. If [Equals(LengthOf(Line(D,F)),2(x+5)-7)] and [Equals(LengthOf(Line(E,G)),3(x-2))] [Find(LengthOf(Line(E,G)))]."
"In the triangle, what is the measure of \angle Z?","In [Triangle($)], [Find(MeasureOf(Angle(Z)))]?"
Find the value of s in the parallelogram.,[Find(s)] in [Parallelogram($)].
Find y.,[Find(y)].
Find x.,[Find(x)].
"Polygon ABCD \sim polygon AEFG, m \angle AGF = 108, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26. Find the perimeter of trapezoid ABCD.","[Similar(Quadrilateral(A,B,C,D),Quadrilateral(A,E,F,G))], [Equals(MeasureOf(Angle(A,G,F)),108)] [Equals(LengthOf(Line(G,F)),14)] [Equals(LengthOf(Line(A,D)),12)] [Equals(LengthOf(Line(D,G)),4.5)] [Equals(LengthOf(Line(E,F)),8)] and [Equals(LengthOf(Line(A,B)),26)] [Find(PerimeterOf(Trapezoid(A,B,C,D)))]."
Polygon BCDE \cong polygon RSTU. Find y.,"[Congruent(Quadrilateral(B,C,D,E),Quadrilateral(R,S,T,U))]. [Find(y)]."
Find the area of the composite figure. Round to the nearest tenth.,[Find(AreaOf(Shape($)))]. Round to nearest tenth.
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
Find x.,[Find(x)].
"In the figure, m \angle 12 = 64. Find the measure of \angle 3.",", [Equals(MeasureOf(Angle(12)),64)] [Find(MeasureOf(Angle(3)))]."
Find the value of d in the parallelogram.,[Find(d)] in [Parallelogram($)].
Find x in the figure.,[Find(x)].
Refer to trapezoid CDFG with median HE. Find GF.,"[Trapezoid(C,D,F,G)], [IsMedianOf(Line(H,E),Trapezoid(C,D,F,G))]. [Find(LengthOf(Line(G,F)))]."
Find EG.,"[Find(LengthOf(Line(E,G)))]."
Find m \angle M.,[Find(MeasureOf(Angle(M)))].
"If EN = 13, what is the diameter of the circle?","If [Equals(LengthOf(Line(E,N)),13)] [Find(DiameterOf(Circle($)))]?"
Find m \angle CGD.,"[Find(MeasureOf(Angle(C,G,D)))]."
Find the area of the triangle. Round to the nearest tenth if necessary.,[Find(AreaOf(Triangle($)))]. Round to nearest tenth if necessary.
Find x. Round to the nearest degree.,[Find(x)]. Round to nearest degree.
Find the exact circumference of the circle.,[Find(CircumferenceOf(Circle($)))].
Find GH.,"[Find(LengthOf(Line(G,H)))]."
"For the pair of similar figures, find the area of the green figure.","[Similar(Shape($1),Shape($2))], [Find(AreaOf(Green(Shape($))))]."
"In the figure, m \angle 3 = 43. Find the measure of \angle 13.",", [Equals(MeasureOf(Angle(3)),43)] [Find(MeasureOf(Angle(13)))]."
"Quadrilateral ABCD is inscribed in \odot Z such that m \angle BZA = 104, m \widehat CB = 94, and AB \parallel DC. Find m \angle BDA.","[InscribedIn(Quadrilateral(A,B,C,D),Circle(Z))] [Equals(MeasureOf(Angle(B,Z,A)),104)] [Equals(MeasureOf(Arc(C,B)),94)] and [Parallel(Line(A,B),Line(D,C))]. [Find(MeasureOf(Angle(B,D,A)))]."
"If a \parallel b in the diagram below, which of the following may not be true?","If [Parallel(Line(a),Line(b))], which of following may not be true?"
Find m \angle M.,[Find(MeasureOf(Angle(M)))].
Q is the incenter of \triangle JKL. Find m \angle QJK.,"[IsIncenterOf(Point(Q),Triangle(J,K,L))]. [Find(MeasureOf(Angle(Q,J,K)))]."
Find x.,[Find(x)].
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Use parallelogram JKLM to find b if JK = 2b+3 and JM = 3a.,"Use [Parallelogram(J,K,L,M)] to [Find(b)] if [Equals(LengthOf(Line(J,K)),2b+3)] and [Equals(LengthOf(Line(J,M)),3a)]."
Find y in the figure.,[Find(y)].
"If m \angle BAD = 38 and m \angle BCD = 50, find m \angle ADC.","If [Equals(MeasureOf(Angle(B,A,D)),38)] and [Equals(MeasureOf(Angle(B,C,D)),50)] [Find(MeasureOf(Angle(A,D,C)))]."
"Quadrilateral ABCD is a rhombus. If m \angle ABC = 2x-7 and m \angle BCD = 2x+3, find m \angle DAB."," [Rhombus(A,B,C,D)]. If [Equals(MeasureOf(Angle(A,B,C)),2x-7)] and [Equals(MeasureOf(Angle(B,C,D)),2x+3)] [Find(MeasureOf(Angle(D,A,B)))]."
Find RT.,"[Find(LengthOf(Line(R,T)))]."
Find m \angle A.,[Find(MeasureOf(Angle(A)))].
"In \odot Z, \angle WZX \cong \angle XZY, m \angle VZU = 4x, m \angle UZY = 2x+24, and VY and WU are diameters. Find m \widehat WX.","In [Circle(Z)], [Equals(Angle(W,Z,X),Angle(X,Z,Y))], [Equals(MeasureOf(Angle(V,Z,U)),4x)] [Equals(MeasureOf(Angle(U,Z,Y)),2x+24)] and [IsDiameterOf(Line(V,Y),Circle($))], [IsDiameterOf(Line(W,U),Circle($))]. [Find(MeasureOf(Arc(W,X)))]."
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
Find the area of the quadrilateral.,[Find(AreaOf(Quadrilateral($)))].
"In the figure, m \angle 9 = 75. Find the measure of \angle 3.",", [Equals(MeasureOf(Angle(9)),75)] [Find(MeasureOf(Angle(3)))]."
Find x so that m \parallel n.,"[Find(x)] so [Parallel(Line(m),Line(n))]."
"Circles G, J, and K all intersect at L. If GH = 10. Find GJ.","[IntersectAt(Circle(G),Circle(J),Circle(K),Point(L))]. If [Equals(LengthOf(Line(G,H)),10)] [Find(LengthOf(Line(G,J)))]."
The area A of the shaded region is given. Find x. A = 128 ft^2.,". [Find(x)]. [Equals(AreaOf(Shape(A)),128)]."
Find m \angle V.,[Find(MeasureOf(Angle(V)))].
"In the figure, m \angle 1 = 123. Find the measure of \angle 6.",", [Equals(MeasureOf(Angle(1)),123)] [Find(MeasureOf(Angle(6)))]."
Find y in the figure.,[Find(y)].
"If m \angle AED = 95 and m \widehat AD = 120, what is m \angle BAC?","If [Equals(MeasureOf(Angle(A,E,D)),95)] and [Equals(MeasureOf(Arc(A,D)),120)] [Find(MeasureOf(Angle(B,A,C)))]?"
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
"If PR \parallel KL, KN = 9, LN = 16, and PM = 2KP, find MN.","If [Parallel(Line(P,R),Line(K,L))], [Equals(LengthOf(Line(K,N)),9)] [Equals(LengthOf(Line(L,N)),16)] and [Equals(LengthOf(Line(P,M)),Mul(Line(K,P),2))], [Find(LengthOf(Line(M,N)))]."
Find YZ.,"[Find(LengthOf(Line(Y,Z)))]."
\triangle LMN \cong \triangle QRS. Find y.,"[Congruent(Triangle(L,M,N),Triangle(Q,R,S))]. [Find(y)]."
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Each pair of polygons is similar. Find ED.,"[Similar(Polygon($1),Polygon($2))]. [Find(LengthOf(Line(E,D)))]."
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
"In \odot G, m \angle AGB = 30 and CG \perp GD. Find m \widehat BC.","In [Circle(G)], [Equals(MeasureOf(Angle(A,G,B)),30)] and [Perpendicular(Line(C,G),Line(G,D))]. [Find(MeasureOf(Arc(B,C)))]."
Find ST.,"[Find(LengthOf(Line(S,T)))]."
Find x so that m \parallel n.,"[Find(x)] so [Parallel(Line(m),Line(n))]."
Find the area of a regular pentagon with a perimeter of 40 centimeters.,"[Find(AreaOf(Regular(Pentagon($))))], [Equals(PerimeterOf(Regular(Pentagon($))),40)]."
Find x.,[Find(x)].
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Find x.,[Find(x)].
Solve for x.,[Find(x)].
\triangle RST \cong \triangle ABC. Find y.,"[Congruent(Triangle(R,S,T),Triangle(A,B,C))]. [Find(y)]."
"Assume that the segment is tangent, find the value of x.","[Tangent(Line($),Circle($))], [Find(x)]."
"ABCD is a rhombus. If EB = 9, AB = 12 and m \angle ABD = 55. Find CE."," [Rhombus(A,B,C,D)]. If [Equals(LengthOf(Line(E,B)),9)] [Equals(LengthOf(Line(A,B)),12)] and [Equals(MeasureOf(Angle(A,B,D)),55)] [Find(LengthOf(Line(C,E)))]."
Find XY.,"[Find(LengthOf(Line(X,Y)))]."
Find x.,[Find(x)].
\triangle KLN and \triangle LMN are isosceles and m \angle JKN = 130. Find the measure of \angle LNM.,"[Isosceles(Triangle(K,L,N))], [Isosceles(Triangle(L,M,N))] and [Equals(MeasureOf(Angle(J,K,N)),130)] [Find(MeasureOf(Angle(L,N,M)))]."
Find RS.,"[Find(LengthOf(Line(R,S)))]."
Quadrilateral WXYZ is a rectangle. Find the measure of \angle 8 if m \angle 1 = 30.," [Rectangle(W,X,Y,Z)]. [Find(MeasureOf(Angle(8)))] if [Equals(MeasureOf(Angle(1)),30)]."
Find the measure of \angle T to the nearest tenth.,[Find(MeasureOf(Angle(T)))] to nearest tenth.
"Given right triangle XYZ with hypotenuse XY, YP is equal to YZ. If m \angle PYZ = 26, find m \angle XZP.","[Right(Triangle(X,Y,Z))], [IsHypotenuseOf(Line(X,Y),Right(Triangle(X,Y,Z)))], [Equals(LengthOf(Line(Y,P)),Line(Y,Z))]. If [Equals(MeasureOf(Angle(P,Y,Z)),26)] [Find(MeasureOf(Angle(X,Z,P)))]."
Find the area of the kite.,[Find(AreaOf(Kite($)))].
Find m \angle X.,[Find(MeasureOf(Angle(X)))].
Find x to the nearest tenth.,[Find(x)] to nearest tenth.
"ABCD is a rhombus. If EB = 9, AB = 12 and m \angle ABD = 55. Find m \angle BDA."," [Rhombus(A,B,C,D)]. If [Equals(LengthOf(Line(E,B)),9)] [Equals(LengthOf(Line(A,B)),12)] and [Equals(MeasureOf(Angle(A,B,D)),55)] [Find(MeasureOf(Angle(B,D,A)))]."
"Find y. Round to the nearest tenth, if necessary.","[Find(y)]. Round to nearest tenth, if necessary."
Find x.,[Find(x)].
Find y.,[Find(y)].
Find x. Round the angle measure to the nearest degree.,[Find(x)]. Round angle measure to nearest degree.
Find m \angle 3.,[Find(MeasureOf(Angle(3)))].
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
find \sin A.,[Find(SinOf(Angle(A)))].
"Find the perimeter of the figure in feet. Round to the nearest tenth, if necessary.","[Find(PerimeterOf(Shape($)))] in. Round to nearest tenth, if necessary."
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
\odot P is inscribed in equilateral triangle LMN. What is the circumference of \odot P?,"[InscribedIn(Circle(P),Equilateral(Triangle(L,M,N)))]. [Find(CircumferenceOf(Circle(P)))]?"
"If AB = 60 and DE = 48, find CF.","If [Equals(LengthOf(Line(A,B)),60)] and [Equals(LengthOf(Line(D,E)),48)] [Find(LengthOf(Line(C,F)))]."
Find m \angle ABC if m \widehat AB = 102.,"[Find(MeasureOf(Angle(A,B,C)))] if [Equals(MeasureOf(Arc(A,B)),102)]."
Find x so that p \parallel q.,"[Find(x)] so [Parallel(Line(p),Line(q))]."
Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.,"[Find(x)] to nearest tenth. [Tangent(Line($),Circle($))]."
"Quadrilateral ABCD is a rhombus. If AP = 3x-1 and PC = x+9, find AC."," [Rhombus(A,B,C,D)]. If [Equals(LengthOf(Line(A,P)),3x-1)] and [Equals(LengthOf(Line(P,C)),x+9)] [Find(LengthOf(Line(A,C)))]."
Use parallelogram ABCD to find m \angle BCD.,"Use [Parallelogram(A,B,C,D)] to [Find(MeasureOf(Angle(B,C,D)))]."
Find x.,[Find(x)].
"If m \angle AFB = 8x-6 and m \angle BFC = 14x+8, find the value of x so that \angle AFC is a right angle.","If [Equals(MeasureOf(Angle(A,F,B)),8x-6)] and [Equals(MeasureOf(Angle(B,F,C)),14x+8)] [Find(x)] so [RightAngle(Angle(A,F,C))]."
Find FH.,"[Find(LengthOf(Line(F,H)))]."
"In the figure, m \angle 3 = 110 and m \angle 12 = 55. Find the measure of \angle 15.",", [Equals(MeasureOf(Angle(3)),110)] and [Equals(MeasureOf(Angle(12)),55)] [Find(MeasureOf(Angle(15)))]."
Find m \angle F.,[Find(MeasureOf(Angle(F)))].
Find x.,[Find(x)].
Find x.,[Find(x)].
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Use parallelogram MNPR to find z.,"Use [Parallelogram(M,N,P,R)] to [Find(z)]."
"Find the area of the figure in feet. Round to the nearest tenth, if necessary.","[Find(AreaOf(Shape($)))] in. Round to nearest tenth, if necessary."
Find x.,[Find(x)].
Rhombus RSTU has an area of 675 square meters. Find SU.,"[Equals(AreaOf(Rhombus(R,S,T,U)),675)] [Find(LengthOf(Line(S,U)))]."
The triangle is inscribed into the circle. Find the exact circumference of the circle.,"[InscribedIn(Triangle($),Circle($))]. [Find(CircumferenceOf(Circle($)))]."
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
"In \odot R, SU = 20, YW = 20, and m \widehat YX = 45. Find SV.","In [Circle(R)], [Equals(LengthOf(Line(S,U)),20)] [Equals(LengthOf(Line(Y,W)),20)] and [Equals(MeasureOf(Arc(Y,X)),45)] [Find(LengthOf(Line(S,V)))]."
Find AC.,"[Find(LengthOf(Line(A,C)))]."
Find the value of x in the figure below.,[Find(x)].
"ABCD is a rhombus. If EB = 9, AB = 12 and m \angle ABD = 55. Find AE."," [Rhombus(A,B,C,D)]. If [Equals(LengthOf(Line(E,B)),9)] [Equals(LengthOf(Line(A,B)),12)] and [Equals(MeasureOf(Angle(A,B,D)),55)] [Find(LengthOf(Line(A,E)))]."
Find y.,[Find(y)].
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find the value of x.,[Find(x)].
"Find x. Round to the nearest tenth, if necessary.","[Find(x)]. Round to nearest tenth, if necessary."
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
Find x.,[Find(x)].
Quadrilateral ABDC is a rectangle. Find m \angle 6 if m \angle 1 = 38.," [Rectangle(A,B,D,C)]. [Find(MeasureOf(Angle(6)))] if [Equals(MeasureOf(Angle(1)),38)]."
"In \triangle CDF, K is the centroid and DK = 16. Find FG."," [Triangle(C,D,F)], [IsCentroidOf(Point(K),Triangle(C,D,F))] and [Equals(LengthOf(Line(D,K)),16)] [Find(LengthOf(Line(F,G)))]."
Find the angle measure of \angle 1.,[Find(MeasureOf(Angle(1)))].
"If EB \parallel DC, find x.","If [Parallel(Line(E,B),Line(D,C))], [Find(x)]."
"Circle O has a radius of 10, AB = 10 and m \overrightarrow AB = 60. Find m \widehat AY.","[Equals(RadiusOf(Circle(O)),10)] [Equals(LengthOf(Line(A,B)),10)] and [Equals(LengthOf(Line(A,B)),60)] [Find(MeasureOf(Arc(A,Y)))]."
Find m \angle ZXV.,"[Find(MeasureOf(Angle(Z,X,V)))]."
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find y.,[Find(y)].
Find JM if \triangle JMN is an isosceles triangle with JM \cong MN.,"[Find(LengthOf(Line(J,M)))] if [Isosceles(Triangle(J,M,N))] with [Equals(LengthOf(Line(J,M)),Line(M,N))]."
ED is tangent to \odot F at point E. Find x.,"[Tangent(Line(E,D),Circle(F))] at [Point(E)]. [Find(x)]."
Find x. Round to the nearest hundredth.,[Find(x)]. Round to nearest hundredth.
"Find the area of the figure in feet. Round to the nearest tenth, if necessary.","[Find(AreaOf(Shape($)))] in. Round to nearest tenth, if necessary."
"In the figure, FJ \cong FH and GF \cong GH. If m \angle GHJ = 152 and m \angle G = 32, find m \angle JFH.",", [Equals(LengthOf(Line(F,J)),Line(F,H))] and [Equals(LengthOf(Line(G,F)),Line(G,H))]. If [Equals(MeasureOf(Angle(G,H,J)),152)] and [Equals(MeasureOf(Angle(G)),32)] [Find(MeasureOf(Angle(J,F,H)))]."
Find m \angle ABD.,"[Find(MeasureOf(Angle(A,B,D)))]."
"a = 14, b = 48, and c = 50, find \sin B.","[Equals(a,14)] [Equals(b,48)] and [Equals(c,50)] [Find(SinOf(Angle(B)))]."
"Find the perimeter of the \triangle DEF, if \triangle DEF \sim \triangle CBF, perimeter of \triangle CBF = 27, DF = 6, FC = 8.","[Find(PerimeterOf(Triangle(D,E,F)))], if [Similar(Triangle(D,E,F),Triangle(C,B,F))], [Equals(PerimeterOf(Triangle(C,B,F)),27)] [Equals(LengthOf(Line(D,F)),6)] [Equals(LengthOf(Line(F,C)),8)]."
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
"In \triangle GHJ, HP = 5x-16, PJ = 3x+8, m \angle GJN = 6y-3, m \angle NJH = 4y+23 and m \angle HMG = 4z+14. If HM is an altitude of \angle GHJ, find the value of z.","In [Triangle(G,H,J)], [Equals(LengthOf(Line(H,P)),5x-16)] [Equals(LengthOf(Line(P,J)),3x+8)] [Equals(MeasureOf(Angle(G,J,N)),6y-3)] [Equals(MeasureOf(Angle(N,J,H)),4y+23)] and [Equals(MeasureOf(Angle(H,M,G)),4z+14)] If [Equals(Line(H,M),AltitudeOf(Angle(G,H,J)))], [Find(z)]."
Find x.,[Find(x)].
"In \odot D, DE \cong EC, m \widehat CF = 60, and DE \perp EC. Find m \angle 5.","In [Circle(D)], [Equals(LengthOf(Line(D,E)),Line(E,C))], [Equals(MeasureOf(Arc(C,F)),60)] and [Perpendicular(Line(D,E),Line(E,C))]. [Find(MeasureOf(Angle(5)))]."
Find the area of the circle. Round to the nearest tenth.,[Find(AreaOf(Circle($)))]. Round to nearest tenth.
Use parallelogram JKLM to find m \angle JML.,"Use [Parallelogram(J,K,L,M)] to [Find(MeasureOf(Angle(J,M,L)))]."
"Quadrilateral WXYZ is a rectangle. If XZ = 2c and ZY = 6, and XY = 8, find WY."," [Rectangle(W,X,Y,Z)]. If [Equals(LengthOf(Line(X,Z)),2c)] and [Equals(LengthOf(Line(Z,Y)),6)] and [Equals(LengthOf(Line(X,Y)),8)] [Find(LengthOf(Line(W,Y)))]."
"In \odot O, EC and AB are diameters, and \angle BOD \cong \angle DOE \cong \angle EOF \cong \angle FOA. Find m \widehat ACB.","[Circle(O)], [IsDiameterOf(Line(E,C),Circle(O))], [IsDiameterOf(Line(A,B),Circle(O))] and [Equals(Angle(B,O,D),Angle(D,O,E))], [Equals(Angle(D,O,E),Angle(E,O,F))], [Equals(Angle(E,O,F),Angle(F,O,A))]. [Find(MeasureOf(Arc(A,C,B)))]."
"Circle A has diameters DF and PG. If PA = 7, find PG.","[IsDiameterOf(Line(D,F),Circle(A))], [IsDiameterOf(Line(P,G),Circle(A))]. If [Equals(LengthOf(Line(P,A)),7)] [Find(LengthOf(Line(P,G)))]."
Find the area of the circle. Round to the nearest tenth.,[Find(AreaOf(Circle($)))]. Round to nearest tenth.
Use parallelogram to find z.,Use [Parallelogram($)] to [Find(z)].
Find y.,[Find(y)].
"For the pair of similar figures, find the area of the green figure.","[Similar(Shape($1),Shape($2))], [Find(AreaOf(Green(Shape($))))]."
"If QR = 2, XW = 12, QW = 15, and ST = 5, find RS.","If [Equals(LengthOf(Line(Q,R)),2)] [Equals(LengthOf(Line(X,W)),12)] [Equals(LengthOf(Line(Q,W)),15)] and [Equals(LengthOf(Line(S,T)),5)] [Find(LengthOf(Line(R,S)))]."
Find x.,[Find(x)].
Find the area of the shaded region formed by the circle and regular polygon. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))] formed by [Circle($)] and [Regular(Polygon($))]. Round to nearest tenth.
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
PQRS is a rhombus inscribed in a circle. Find m \angle QRP.," [InscribedIn(Rhombus(P,Q,R,S),Circle($))]. [Find(MeasureOf(Angle(Q,R,P)))]."
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
"For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure.","[Similar(Shape($1),Shape($2))], to [Find(ScaleFactorOf(Blue(Shape($)),Green(Shape($))))]."
Find x.,[Find(x)].
"In the figure, m \angle 1 = 50 and m \angle 3 = 60. Find the measure of \angle 5.",", [Equals(MeasureOf(Angle(1)),50)] and [Equals(MeasureOf(Angle(3)),60)] [Find(MeasureOf(Angle(5)))]."
Find m \angle T.,[Find(MeasureOf(Angle(T)))].
Find m \angle C.,[Find(MeasureOf(Angle(C)))].
What is the length of EF?,"[Find(LengthOf(Line(E,F)))]?"
"Find JL, if KP = 4 and PM = 7.","[Find(LengthOf(Line(J,L)))], if [Equals(LengthOf(Line(K,P)),4)] and [Equals(LengthOf(Line(P,M)),7)]."
"In \triangle RST, Z is the centroid and RZ = 18. Find ZV."," [Triangle(R,S,T)], [IsCentroidOf(Point(Z),Triangle(R,S,T))] and [Equals(LengthOf(Line(R,Z)),18)] [Find(LengthOf(Line(Z,V)))]."
Find the area of the regular polygon. Round to the nearest tenth.,[Find(AreaOf(Regular(Polygon($))))]. Round to nearest tenth.
"In the figure consisting of squares A, B, and C, JK = 2KL and KL = 2LM. If the perimeter of the figure is 66 units, what is the area?","consisting of [Square(A)], [Square(B)] and [Square(C)], [Equals(LengthOf(Line(J,K)),Mul(Line(K,L),2))] and [Equals(LengthOf(Line(K,L)),Mul(Line(L,M),2))]. If [Equals(PerimeterOf(Shape($)),66)] [Find(AreaOf(Polygon($)))]?"
Refer to the figure at the right. Find the value of y if p \parallel q.,"[Shape($)]. [Find(y)] if [Parallel(Line(p),Line(q))]."
Find the area of the triangle. Round to the nearest hundredth.,[Find(AreaOf(Triangle($)))]. Round to nearest hundredth.
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Use parallelogram ABCD to find m \angle AFB.,"Use [Parallelogram(A,B,C,D)] to [Find(MeasureOf(Angle(A,F,B)))]."
"If m \angle 2 = 70-4x and m \angle 5 = 18x-8, find m \angle 5.","If [Equals(MeasureOf(Angle(2)),70-4x)] and [Equals(MeasureOf(Angle(5)),18x-8)] [Find(MeasureOf(Angle(5)))]."
"If the polygon shown is regular, what is m \angle ABC.","If [Regular(Polygon($))], [Find(MeasureOf(Angle(A,B,C)))]."
Find x.,[Find(x)].
"In the figure, m \angle 1 = 50 and m \angle 3 = 60. Find the measure of \angle 7.",", [Equals(MeasureOf(Angle(1)),50)] and [Equals(MeasureOf(Angle(3)),60)] [Find(MeasureOf(Angle(7)))]."
Find x so that p \parallel q.,"[Find(x)] so [Parallel(Line(p),Line(q))]."
Find x. Round side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
"If QRST is a parallelogram, what is the value of x?","If [Parallelogram(Q,R,S,T)], [Find(x)]?"
Find x.,[Find(x)].
"In \odot O, EC and AB are diameters, and \angle BOD \cong \angle DOE \cong \angle EOF \cong \angle FOA. Find m \widehat EB.","[Circle(O)], [IsDiameterOf(Line(E,C),Circle(O))], [IsDiameterOf(Line(A,B),Circle(O))] and [Equals(Angle(B,O,D),Angle(D,O,E))], [Equals(Angle(D,O,E),Angle(E,O,F))], [Equals(Angle(E,O,F),Angle(F,O,A))]. [Find(MeasureOf(Arc(E,B)))]."
"Find WT, if ZX = 20 and TY = 15.","[Find(LengthOf(Line(W,T)))], if [Equals(LengthOf(Line(Z,X)),20)] and [Equals(LengthOf(Line(T,Y)),15)]."
Find x.,[Find(x)].
Find PQ.,"[Find(LengthOf(Line(P,Q)))]."
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
What is the area of the figure? Round to the nearest tenth.,[Find(AreaOf(Shape($)))]? Round to nearest tenth.
Find the area of the shaded sector. Round to the nearest tenth.,[Find(AreaOf(Shaded(Sector($))))]. Round to nearest tenth.
Find z.,[Find(z)].
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Find z.,[Find(z)].
Find x. Round the side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
Find m \angle S.,[Find(MeasureOf(Angle(S)))].
Solve for x in the figure below.,[Find(x)].
"In \odot F, FH \cong FL and FK = 17. Find LK.","In [Circle(F)], [Equals(LengthOf(Line(F,H)),Line(F,L))] and [Equals(LengthOf(Line(F,K)),17)] [Find(LengthOf(Line(L,K)))]."
"If LN = 12.4, what is JM?","If [Equals(LengthOf(Line(L,N)),12.4)] [Find(LengthOf(Line(J,M)))]?"
Find the value of x in the diagram.,[Find(x)].
Find x. A = 78 cm^2.,"[Find(x)]. [Equals(AreaOf(Shape(A)),78)]."
"In \odot A, m \angle EAD = 42. Find m \widehat EDB.","In [Circle(A)], [Equals(MeasureOf(Angle(E,A,D)),42)] [Find(MeasureOf(Arc(E,D,B)))]."
Find x.,[Find(x)].
"Use parallelogram to, find a.",Use [Parallelogram($)] to [Find(a)].
Find x.,[Find(x)].
"In the figure, JM \cong PM and ML \cong PL. If m \angle PLJ = 58, find m \angle PJL.",", [Equals(LengthOf(Line(J,M)),Line(P,M))] and [Equals(LengthOf(Line(M,L)),Line(P,L))]. If [Equals(MeasureOf(Angle(P,L,J)),58)] [Find(MeasureOf(Angle(P,J,L)))]."
Find x. Round to the nearest hundredth.,[Find(x)]. Round to nearest hundredth.
Each pair of polygons is similar. Find EG.,"[Similar(Polygon($1),Polygon($2))]. [Find(LengthOf(Line(E,G)))]."
The segment is tangent to the circle. Find x.,"[Tangent(Line($),Circle($))] to [Circle($)]. [Find(x)]."
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
"UJ = 9, VJ = 3, and ZT = 18. Find ZJ.","[Equals(LengthOf(Line(U,J)),9)] [Equals(LengthOf(Line(V,J)),3)] and [Equals(LengthOf(Line(Z,T)),18)] [Find(LengthOf(Line(Z,J)))]."
"In \odot D, DE \cong EC, m \widehat CF = 60, and DE \perp EC. Find m \widehat AF.","In [Circle(D)], [Equals(LengthOf(Line(D,E)),Line(E,C))], [Equals(MeasureOf(Arc(C,F)),60)] and [Perpendicular(Line(D,E),Line(E,C))]. [Find(MeasureOf(Arc(A,F)))]."
Find \angle 6.,[Find(MeasureOf(Angle(6)))].
Find y in the figure.,[Find(y)].
Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. [Regular(Polygon($))]. Round to nearest tenth.
"For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure.","[Similar(Shape($1),Shape($2))], to [Find(ScaleFactorOf(Blue(Shape($)),Green(Shape($))))]."
Find JL.,"[Find(LengthOf(Line(J,L)))]."
Find x.,[Find(x)].
"For the pair of similar figures, use the given areas to find the scale factor from the blue to the green figure.","[Similar(Shape($1),Shape($2))], to [Find(ScaleFactorOf(Blue(Shape($)),Green(Shape($))))]."
Find z.,[Find(z)].
PM is a diameter of \odot R. Find m \widehat MNP.,"[IsDiameterOf(Line(P,M),Circle(R))]. [Find(MeasureOf(Arc(M,N,P)))]."
"For the pair of similar figures, use the given areas to find the scale factor from the blue to the green figure.","[Similar(Shape($1),Shape($2))], to [Find(ScaleFactorOf(Blue(Shape($)),Green(Shape($))))]."
Use parallelogram ABCD to find AB.,"Use [Parallelogram(A,B,C,D)] to [Find(LengthOf(Line(A,B)))]."
Find the measure of \angle 4 if m \angle 4 = m \angle 5.,"[Find(MeasureOf(Angle(4)))] if [Equals(MeasureOf(Angle(4)),MeasureOf(Angle(5)))]."
Find SR.,"[Find(LengthOf(Line(S,R)))]."
Find m \angle AGE.,"[Find(MeasureOf(Angle(A,G,E)))]."
What is the perimeter of the triangle shown below? Round to the nearest tenth.,[Find(PerimeterOf(Triangle($)))]? Round to nearest tenth.
Find x.,[Find(x)].
Find m \angle v.,[Find(LengthOf(Line(m)))] \[Angle($)] [Line(v)].
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
What is the area of the triangle? Round your answer to the nearest tenth if necessary.,[Find(AreaOf(Triangle($)))]? Round to nearest tenth if necessary.
Find the area of the figure. Round to the nearest tenth.,[Find(AreaOf(Shape($)))]. Round to nearest tenth.
Find the perimeter of \triangle DEF if \triangle DEF \sim \triangle ABC.,"[Find(PerimeterOf(Triangle(D,E,F)))] if [Similar(Triangle(D,E,F),Triangle(A,B,C))]."
"The degree measure of minor arc \widehat AC and major arc \widehat ADC are x and y respectively. If m \angle ABC = 70, find y.","degree measure ofinor arc [Arc(A,C)] and major arc [Arc(A,D,C)] are x and y. If [Equals(MeasureOf(Angle(A,B,C)),70)] [Find(y)]."
"Points P, Q, and R are the midpoints of JK, KL, and JL, respectively. Find x.","[IsMidpointOf(Point(P),Line(J,K))], [IsMidpointOf(Point(Q),Line(K,L))], [IsMidpointOf(Point(R),Line(J,L))],,. [Find(x)]."
Find NP.,"[Find(LengthOf(Line(N,P)))]."
Find x.,[Find(x)].
"If TP = 4x+2, QP = 2y-6, PS = 5y-12, and PR = 6x-4, find y so that the quadrilateral is a parallelogram.","If [Equals(LengthOf(Line(T,P)),4x+2)] [Equals(LengthOf(Line(Q,P)),2y-6)] [Equals(LengthOf(Line(P,S)),5y-12)] and [Equals(LengthOf(Line(P,R)),6x-4)] [Find(y)] so [Parallelogram($)]"
Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. [Regular(Polygon($))]. Round to nearest tenth.
"In \triangle CDF, K is the centroid and DK = 16. Find KH."," [Triangle(C,D,F)], [IsCentroidOf(Point(K),Triangle(C,D,F))] and [Equals(LengthOf(Line(D,K)),16)] [Find(LengthOf(Line(K,H)))]."
Find x.,[Find(x)].
Find the measure of \angle 4 if AB \perp BC.,"[Find(MeasureOf(Angle(4)))] if [Perpendicular(Line(A,B),Line(B,C))]."
Use parallelogram JKLM to find a if JK = 2b+3 and JM = 3a.,"Use [Parallelogram(J,K,L,M)] to [Find(a)] if [Equals(LengthOf(Line(J,K)),2b+3)] and [Equals(LengthOf(Line(J,M)),3a)]."
Find m \angle R.,[Find(MeasureOf(Angle(R)))].
Find x.,[Find(x)].
Find x. Assume that any segment that appears to be tangent is tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
"Lines l, m, and n are perpendicular bisectors of \triangle PQR and meet at T. If TQ = 2x, PT = 3y-1, and TR = 8, find x.","[IsPerpendicularBisectorOf(Line(l),Triangle(P,Q,R))], [IsPerpendicularBisectorOf(Line(m),Triangle(P,Q,R))], [IsPerpendicularBisectorOf(Line(n),Triangle(P,Q,R))]. [IntersectAt(Line(l),Line(m),Line(n),Point(T))]. If [Equals(LengthOf(Line(T,Q)),2x)] [Equals(LengthOf(Line(P,T)),3y-1)] and [Equals(LengthOf(Line(T,R)),8)] [Find(x)]."
"In the figure, m \angle 11 = 62 and m \angle 14 = 38. Find the measure of \angle 4.",", [Equals(MeasureOf(Angle(11)),62)] and [Equals(MeasureOf(Angle(14)),38)] [Find(MeasureOf(Angle(4)))]."
Find XZ of isosceles \triangle XYZ.,"[Find(LengthOf(Line(X,Z)))] of [Isosceles(Triangle(X,Y,Z))]."
"Use rhombus XYZW with m \angle WYZ = 53, VW = 3, XV = 2a-2, and ZV = \frac{5a+1}{4}. Find XZ.","Use [Rhombus(X,Y,Z,W)] with [Equals(MeasureOf(Angle(W,Y,Z)),53)] [Equals(LengthOf(Line(V,W)),3)] [Equals(LengthOf(Line(X,V)),2a-2)] and [Equals(LengthOf(Line(Z,V)),\frac{5a+1}{4})] [Find(LengthOf(Line(X,Z)))]."
Find x.,[Find(x)].
Find the area of the figure. Round to the nearest tenth.,[Find(AreaOf(Shape($)))]. Round to nearest tenth.
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
"Quadrilateral DEFG is a rectangle. If DE = 14+2x and GF = 4(x-3)+6, find GF."," [Rectangle(D,E,F,G)]. If [Equals(LengthOf(Line(D,E)),14+2x)] and [Equals(LengthOf(Line(G,F)),4(x-3)+6)] [Find(LengthOf(Line(G,F)))]."
Find x.,[Find(x)].
m \angle 4 = 32. Find the measure of \angle 3.,"[Equals(MeasureOf(Angle(4)),32)] [Find(MeasureOf(Angle(3)))]."
"Quadrilateral ABCD is a rhombus. If m \angle BCD = 120, find m \angle DAC."," [Rhombus(A,B,C,D)]. If [Equals(MeasureOf(Angle(B,C,D)),120)] [Find(MeasureOf(Angle(D,A,C)))]."
"Find the area of the shaded sector. Round to the nearest tenth, if necessary.","[Find(AreaOf(Shaded(Sector($))))]. Round to nearest tenth, if necessary."
The triangle is inscribed in \odot D. Find the exact circumference of \odot D.,"[InscribedIn(Triangle($),Circle(D))]. [Find(CircumferenceOf(Circle(D)))]."
Use parallelogram MNPR to find w.,"Use [Parallelogram(M,N,P,R)] to [Find(w)]."
Find x.,[Find(x)].
Quadrilateral ABCD is a rectangle. Find x.," [Rectangle(A,B,C,D)]. [Find(x)]."
Find x.,[Find(x)].
"If QT = 11, what is QU.","If [Equals(LengthOf(Line(Q,T)),11)] [Find(LengthOf(Line(Q,U)))]."
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
What is ED?,"[Find(LengthOf(Line(E,D)))]?"
"For trapezoid ABCD, S and T are midpoints of the legs. If AB = 3x, ST = 15, and CD = 9x, find x.","[Trapezoid(A,B,C,D)], [IsMidpointOf(Point(S),LegOf(Trapezoid(A,B,C,D)))], [IsMidpointOf(Point(T),LegOf(Trapezoid(A,B,C,D)))],. If [Equals(LengthOf(Line(A,B)),3x)] [Equals(LengthOf(Line(S,T)),15)] and [Equals(LengthOf(Line(C,D)),9x)] [Find(x)]."
"In \odot G, m \angle AGB = 30 and CG \perp GD. Find m \widehat FD.","In [Circle(G)], [Equals(MeasureOf(Angle(A,G,B)),30)] and [Perpendicular(Line(C,G),Line(G,D))]. [Find(MeasureOf(Arc(F,D)))]."
Find m \widehat TS.,"[Find(MeasureOf(Arc(T,S)))]."
Find y.,[Find(y)].
Find m \angle E.,[Find(MeasureOf(Angle(E)))].
"ABCD is a trapezoid. If AC = 3x-7 and BD = 2x+8, find the value of x so that ABCD is isosceles."," [Trapezoid(A,B,C,D)]. If [Equals(LengthOf(Line(A,C)),3x-7)] and [Equals(LengthOf(Line(B,D)),2x+8)] [Find(x)] so [Isosceles(Quadrilateral(A,B,C,D))]."
Find x.,[Find(x)].
Find the area of the figure.,[Find(AreaOf(Shape($)))].
\triangle KLN and \triangle LMN are isosceles and m \angle JKN = 130. Find the measure of \angle LKN.,"[Isosceles(Triangle(K,L,N))], [Isosceles(Triangle(L,M,N))] and [Equals(MeasureOf(Angle(J,K,N)),130)] [Find(MeasureOf(Angle(L,K,N)))]."
Find the area of the figure. Round to the nearest tenth.,[Find(AreaOf(Shape($)))]. Round to nearest tenth.
Find x in the parallelogram.,[Find(x)] in [Parallelogram($)].
Find y.,[Find(y)].
"Find the area of the figure. Round to the nearest tenth, if necessary.","[Find(AreaOf(Shape($)))]. Round to nearest tenth, if necessary."
Find the area of the figure. Round to the nearest tenth.,[Find(AreaOf(Shape($)))]. Round to nearest tenth.
Find x.,[Find(x)].
Find the value of the variable x in the figure.,[Find(x)].
"In \odot R, SU = 20, YW = 20, and m \widehat YX = 45. Find WZ.","In [Circle(R)], [Equals(LengthOf(Line(S,U)),20)] [Equals(LengthOf(Line(Y,W)),20)] and [Equals(MeasureOf(Arc(Y,X)),45)] [Find(LengthOf(Line(W,Z)))]."
Find y.,[Find(y)].
Find the measure of the altitude drawn to the hypotenuse.,"[Find(LengthOf(AltitudeOf(Triangle($1,$2,$3))))], [IsHypotenuseOf(Line($1,$3),Triangle($1,$2,$3))]."
"In the figure, m \angle 1 = 53. Find the measure of \angle 4.",", [Equals(MeasureOf(Angle(1)),53)] [Find(MeasureOf(Angle(4)))]."
Find the value of x.,[Find(x)].
The area A of the shaded region is given. Find x. A = 94 in^2.,". [Find(x)]. [Equals(AreaOf(Shape(A)),94)]."
Suppose BD = 12 millimeters. Find the radius of the circle.,"[Equals(LengthOf(Line(B,D)),12)] [Find(RadiusOf(Circle($)))]."
Find x.,[Find(x)].
"In \odot R, SU = 20, YW = 20, and m \widehat YX = 45. Find UV.","In [Circle(R)], [Equals(LengthOf(Line(S,U)),20)] [Equals(LengthOf(Line(Y,W)),20)] and [Equals(MeasureOf(Arc(Y,X)),45)] [Find(LengthOf(Line(U,V)))]."
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
Parallelogram MNPQ is shown. What is the value of x?,"[Parallelogram(M,N,P,Q)] is. [Find(x)]?"
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Find CD.,"[Find(LengthOf(Line(C,D)))]."
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Find x.,[Find(x)].
Find x.,[Find(x)].
Find the measure of \angle 3.,[Find(MeasureOf(Angle(3)))].
"The diagonals of rectangle ABCD the have a length of 56 feet. If m \angle BAC = 42, what is the length of AB to the nearest tenth of a foot?","[Rectangle(A,B,C,D)], [IsDiagonalOf(Line(A,C),Rectangle(A,B,C,D))], [IsDiagonalOf(Line(B,D),Rectangle(A,B,C,D))], [Equals(LengthOf(Line(A,C)),56)] [Equals(LengthOf(Line(B,D)),56)] If [Equals(MeasureOf(Angle(B,A,C)),42)] [Find(LengthOf(Line(A,B)))] to nearest tenth of foot?"
Find QS.,"[Find(LengthOf(Line(Q,S)))]."
Find the area of the shaded figure in square inches. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))] in. Round to nearest tenth.
Find CB.,"[Find(LengthOf(Line(C,B)))]."
Find x.,[Find(x)].
"For trapezoid QRTU, V and S are midpoints of the legs. If QR = 12 and UT = 22, find VS.","[Trapezoid(Q,R,T,U)], [IsMidpointOf(Point(V),LegOf(Trapezoid(Q,R,T,U)))], [IsMidpointOf(Point(S),LegOf(Trapezoid(Q,R,T,U)))],. If [Equals(LengthOf(Line(Q,R)),12)] and [Equals(LengthOf(Line(U,T)),22)] [Find(LengthOf(Line(V,S)))]."
Find m \angle E.,[Find(MeasureOf(Angle(E)))].
Use a calculator to find the measure of \angle J to the nearest degree.,to [Find(MeasureOf(Angle(J)))] to nearest degree.
"In \odot P, PS = 4, find the length of \widehat QR. Round to the nearest hundredth.","In [Circle(P)], [Equals(LengthOf(Line(P,S)),4)] [Find(LengthOf(Arc(Q,R)))]. Round to nearest hundredth."
"Polygon ABCD \sim polygon AEFG, m \angle AGF = 108, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26. Find scale factor of trapezoid ABCD to trapezoid AEFG.","[Similar(Quadrilateral(A,B,C,D),Quadrilateral(A,E,F,G))], [Equals(MeasureOf(Angle(A,G,F)),108)] [Equals(LengthOf(Line(G,F)),14)] [Equals(LengthOf(Line(A,D)),12)] [Equals(LengthOf(Line(D,G)),4.5)] [Equals(LengthOf(Line(E,F)),8)] and [Equals(LengthOf(Line(A,B)),26)] [Find(ScaleFactorOf(Trapezoid(A,B,C,D),Trapezoid(A,E,F,G)))]."
Find x.,[Find(x)].
"WXYZ is a square. If WT = 3, find m \angle WTZ."," [Square(W,X,Y,Z)]. If [Equals(LengthOf(Line(W,T)),3)] [Find(MeasureOf(Angle(W,T,Z)))]."
Find m \angle 3.,[Find(MeasureOf(Angle(3)))].
Find the measure of \angle 4 if m \angle DGF = 53 and m \angle AGC = 40.,"[Find(MeasureOf(Angle(4)))] if [Equals(MeasureOf(Angle(D,G,F)),53)] and [Equals(MeasureOf(Angle(A,G,C)),40)]."
Express the ratio of \sin A as a decimal to the nearest hundredth.,[Find(RatioOf(SinOf(Angle(A))))] to nearest hundredth.
Find x. (Hint: Draw an auxiliary line).,[Find(x)]. (Hint: Draw auxiliary line).
"For isosceles trapezoid XYZW, find the length of the median.","[Isosceles(Trapezoid(X,Y,Z,W))], [Find(MedianOf(Isosceles(Trapezoid(X,Y,Z,W))))]."
Find y.,[Find(y)].
Find SP.,"[Find(LengthOf(Line(S,P)))]."
Find x.,[Find(x)].
Express the ratio of \sin L as a decimal to the nearest hundredth.,[Find(RatioOf(SinOf(Angle(L))))] to nearest hundredth.
Use parallelogram ABCD to find AF.,"Use [Parallelogram(A,B,C,D)] to [Find(LengthOf(Line(A,F)))]."
\triangle WXY and \triangle XYZ are isosceles and m \angle XYZ = 128. Find the measure of \angle YZX.,"[Isosceles(Triangle(W,X,Y))], [Isosceles(Triangle(X,Y,Z))] and [Equals(MeasureOf(Angle(X,Y,Z)),128)] [Find(MeasureOf(Angle(Y,Z,X)))]."
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
Find z.,[Find(z)].
"In the figure, \triangle FGH is a right triangle with hypotenuse FH and GJ = GH. What is the measure of \angle JGH?",", [Right(Triangle(F,G,H))], [IsHypotenuseOf(Line(F,H),Right(Triangle(F,G,H)))] and [Equals(LengthOf(Line(G,J)),Line(G,H))]. [Find(MeasureOf(Angle(J,G,H)))]?"
"For the pair of similar figures, use the given areas to find x.","[Similar(Shape($1),Shape($2))], to [Find(x)]."
Find \angle 7.,[Find(MeasureOf(Angle(7)))].
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
"Find the perimeter of the figure in feet. Round to the nearest tenth, if necessary.","[Find(PerimeterOf(Shape($)))] in. Round to nearest tenth, if necessary."
Find the area of the regular polygon. Round to the nearest tenth.,[Find(AreaOf(Regular(Polygon($))))]. Round to nearest tenth.
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
Find x.,[Find(x)].
Find x.,[Find(x)].
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
Find m \angle 3.,[Find(MeasureOf(Angle(3)))].
"In \odot P, PD = 10, PQ = 10, and QE = 20, find PE.","In [Circle(P)], [Equals(LengthOf(Line(P,D)),10)] [Equals(LengthOf(Line(P,Q)),10)] and [Equals(LengthOf(Line(Q,E)),20)] [Find(LengthOf(Line(P,E)))]."
"In \odot A, m \angle EAD = 42. Find m \widehat BC.","In [Circle(A)], [Equals(MeasureOf(Angle(E,A,D)),42)] [Find(MeasureOf(Arc(B,C)))]."
Find the area of the kite.,[Find(AreaOf(Kite($)))].
Find SW.,"[Find(LengthOf(Line(S,W)))]."
Express the ratio of \sin A as a decimal to the nearest hundredth.,[Find(RatioOf(SinOf(Angle(A))))] to nearest hundredth.
"In \odot X, AB = 30, CD = 30, and m \widehat CZ = 40. Find m \widehat DZ.","In [Circle(X)], [Equals(LengthOf(Line(A,B)),30)] [Equals(LengthOf(Line(C,D)),30)] and [Equals(MeasureOf(Arc(C,Z)),40)] [Find(MeasureOf(Arc(D,Z)))]."
Solve for x in the figure below.,[Find(x)].
Find FB if SA and FB are altitudes and \triangle RST \sim \triangle EFG.,"[Find(LengthOf(Line(F,B)))] if [IsAltitudeOf(Line(S,A),Shape($))], [IsAltitudeOf(Line(F,B),Shape($))] and [Similar(Triangle(R,S,T),Triangle(E,F,G))]."
"If m \widehat BC = 30 and AB \cong \widehat CD, find m \widehat AB.","If [Equals(MeasureOf(Arc(B,C)),30)] and [Congruent(Line(A,B),Arc(C,D))], [Find(MeasureOf(Arc(A,B)))]."
Find the area of the triangle. Round to the nearest hundredth.,[Find(AreaOf(Triangle($)))]. Round to nearest hundredth.
"Use the figure to find the indicated variable. If m \angle 4 = 2x-17 and m \angle 1 = 85, find x.","to. If [Equals(MeasureOf(Angle(4)),2x-17)] and [Equals(MeasureOf(Angle(1)),85)] [Find(x)]."
"In the figure, m \angle 1 = 123. Find the measure of \angle 16.",", [Equals(MeasureOf(Angle(1)),123)] [Find(MeasureOf(Angle(16)))]."
Find SC.,"[Find(LengthOf(Line(S,C)))]."
Find m \angle 3.,[Find(MeasureOf(Angle(3)))].
"In \odot Z, \angle WZX \cong \angle XZY, m \angle VZU = 4x, m \angle UZY = 2x+24, and VY and WU are diameters. Find m \widehat WV.","In [Circle(Z)], [Equals(Angle(W,Z,X),Angle(X,Z,Y))], [Equals(MeasureOf(Angle(V,Z,U)),4x)] [Equals(MeasureOf(Angle(U,Z,Y)),2x+24)] and [IsDiameterOf(Line(V,Y),Circle($))], [IsDiameterOf(Line(W,U),Circle($))]. [Find(MeasureOf(Arc(W,V)))]."
Find x. Assume that any segment that appears to be tangent is tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
JH is a midsegment of \triangle KLM. Find x.,"[IsMidsegmentOf(Line(J,H),Triangle(K,L,M))]. [Find(x)]."
"In the figure, m \angle 1 = 53. Find the measure of \angle 2.",", [Equals(MeasureOf(Angle(1)),53)] [Find(MeasureOf(Angle(2)))]."
Find m \angle D.,[Find(MeasureOf(Angle(D)))].
"In quadrilateral PQRS, PQ = 721, QR = 547, RS = 593, PS = 756, and m \angle P = 58. Find QS.","In [Quadrilateral(P,Q,R,S)], [Equals(LengthOf(Line(P,Q)),721)] [Equals(LengthOf(Line(Q,R)),547)] [Equals(LengthOf(Line(R,S)),593)] [Equals(LengthOf(Line(P,S)),756)] and [Equals(MeasureOf(Angle(P)),58)] [Find(LengthOf(Line(Q,S)))]."
"For the pair of similar figures, use the given areas to find the scale factor from the blue to the green figure.","[Similar(Shape($1),Shape($2))], to [Find(ScaleFactorOf(Blue(Shape($)),Green(Shape($))))]."
"If J, P, and L are the midpoints of KH, HM and MK, respectively. Find x.","If [IsMidpointOf(Point(J),Line(K,H))], [IsMidpointOf(Point(P),Line(H,M))], [IsMidpointOf(Point(L),Line(M,K))],,. [Find(x)]."
"For trapezoid QRST, M and P are midpoints of the legs. If QR = 16, PM = 12, and TS = 4x, find x.","[Trapezoid(Q,R,S,T)], [IsMidpointOf(Point(M),LegOf(Trapezoid(Q,R,S,T)))], [IsMidpointOf(Point(P),LegOf(Trapezoid(Q,R,S,T)))],. If [Equals(LengthOf(Line(Q,R)),16)] [Equals(LengthOf(Line(P,M)),12)] and [Equals(LengthOf(Line(T,S)),4x)] [Find(x)]."
"One side of a square is a diameter of a circle. The length of one side of the square is 5 feet. To the nearest hundredth, what is the probability that a point chosen at random is in the shaded region?","One [IsDiameterOf(SideOf(Square($)),Circle($))]. length of one [Equals(SideOf(Square($)),5)] To nearest hundredth, Find probability a point chosen at random is in [Shaded(Shape($))]?"
"In the figure, m \angle 1 = 3a+40, m \angle 2 = 2a+25, and m \angle 3 = 5b-26. Find b.",", [Equals(MeasureOf(Angle(1)),3a+40)] [Equals(MeasureOf(Angle(2)),2a+25)] and [Equals(MeasureOf(Angle(3)),5b-26)] [Find(b)]."
"Find the area of the figure. Round to the nearest hundredth, if necessary.","[Find(AreaOf(Shape($)))]. Round to nearest hundredth, if necessary."
"Quadrilateral WXYZ is a rectangle. If ZY = 2x+3 and WX = x+4, find WX."," [Rectangle(W,X,Y,Z)]. If [Equals(LengthOf(Line(Z,Y)),2x+3)] and [Equals(LengthOf(Line(W,X)),x+4)] [Find(LengthOf(Line(W,X)))]."
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
What is the value of x if m \widehat NR = 62 and m \widehat NP = 108?,"[Find(x)] if [Equals(MeasureOf(Arc(N,R)),62)] and [Equals(MeasureOf(Arc(N,P)),108)]?"
"If a = 10\sqrt{3}, find CE.","If [Equals(a,10\sqrt{3})] [Find(LengthOf(Line(C,E)))]."
"In the figure, m \angle 1 = 123. Find the measure of \angle 4.",", [Equals(MeasureOf(Angle(1)),123)] [Find(MeasureOf(Angle(4)))]."
Find y.,[Find(y)].
"If m \angle 2 = 4x+7 and m \angle 7 = 5x-13, find x.","If [Equals(MeasureOf(Angle(2)),4x+7)] and [Equals(MeasureOf(Angle(7)),5x-13)] [Find(x)]."
Find m \widehat BX.,"[Find(MeasureOf(Arc(B,X)))]."
Find x so that m \parallel n.,"[Find(x)] so [Parallel(Line(m),Line(n))]."
"Find the perimeter of \triangle PQR, if \triangle PQM \sim \triangle PRQ.","[Find(PerimeterOf(Triangle(P,Q,R)))], if [Similar(Triangle(P,Q,M),Triangle(P,R,Q))]."
JH is tangent to \odot G at J. Find the value of x.,"[Tangent(Line(J,H),Circle(G))] at J. [Find(x)]."
"Circles G, J, and K all intersect at L. If GH = 10, find JK.","[IntersectAt(Circle(G),Circle(J),Circle(K),Point(L))]. If [Equals(LengthOf(Line(G,H)),10)] [Find(LengthOf(Line(J,K)))]."
Find m \angle X.,[Find(MeasureOf(Angle(X)))].
Find the measure of \angle 1 if m \angle DGF = 53 and m \angle AGC = 40.,"[Find(MeasureOf(Angle(1)))] if [Equals(MeasureOf(Angle(D,G,F)),53)] and [Equals(MeasureOf(Angle(A,G,C)),40)]."
XY and XZ are midsegments of \triangle RST. Find XZ.,"[IsMidsegmentOf(Line(X,Y),Triangle(R,S,T))], [IsMidsegmentOf(Line(X,Z),Triangle(R,S,T))]. [Find(LengthOf(Line(X,Z)))]."
Find y.,[Find(y)].
Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.,"[Find(x)] to nearest tenth. [Tangent(Line($),Circle($))]."
"If PR \parallel KL, KN = 9, LN = 16, PM = 2 KP, find MR.","If [Parallel(Line(P,R),Line(K,L))], [Equals(LengthOf(Line(K,N)),9)] [Equals(LengthOf(Line(L,N)),16)] [Equals(LengthOf(Line(P,M)),Mul(Line(K,P),2))], [Find(LengthOf(Line(M,R)))]."
EC and AB are diameters of \odot O. Find its measure of \widehat EB.,"[IsDiameterOf(Line(E,C),Circle(O))], [IsDiameterOf(Line(A,B),Circle(O))]. [Find(MeasureOf(Arc(E,B)))]."
Express the ratio of \sin C as a decimal to the nearest hundredth.,[Find(RatioOf(SinOf(Angle(C))))] to nearest hundredth.
Find m \angle F.,[Find(MeasureOf(Angle(F)))].
Find AB.,"[Find(LengthOf(Line(A,B)))]."
Find x. Assume that any segment that appears to be tangent is tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find \widehat DG if m \angle DGI = 24 and r = 6.,"[Find(Arc(D,G))] if [Equals(MeasureOf(Angle(D,G,I)),24)] and [Equals(r,6)]."
Find m \angle 3.,[Find(MeasureOf(Angle(3)))].
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
Find x.,[Find(x)].
Find x.,[Find(x)].
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
Find the length of FG.,"[Find(LengthOf(Line(F,G)))]."
"If WP is a median and an angle bisector, AP = 3y+11, PH = 7y-5, m \angle HWP = x+12, m \angle PAW = 3x-2, and m \angle HWA = 4x-16, find x.","If [IsMedianOf(Line(W,P),Shape($))], [BisectsAngle(Line(W,P),Angle($))], [Equals(LengthOf(Line(A,P)),3y+11)] [Equals(LengthOf(Line(P,H)),7y-5)] [Equals(MeasureOf(Angle(H,W,P)),x+12)] [Equals(MeasureOf(Angle(P,A,W)),3x-2)] and [Equals(MeasureOf(Angle(H,W,A)),4x-16)] [Find(x)]."
Express the ratio of \tan P as a decimal to the nearest hundredth.,[Find(RatioOf(TanOf(Angle(P))))] to nearest hundredth.
Find the measure of the altitude drawn to the hypotenuse.,"[Find(LengthOf(AltitudeOf(Triangle($1,$2,$3))))], [IsHypotenuseOf(Line($1,$3),Triangle($1,$2,$3))]."
Find the value of x.,[Find(x)].
Find x.,[Find(x)].
Find the area of the triangle. Round to the nearest tenth if necessary.,[Find(AreaOf(Triangle($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
Find x.,[Find(x)].
"In \triangle ABC, AD and DC are angle bisectors and m \angle B = 76. What is the measure of \angle ADC?","[Triangle(A,B,C)], [BisectsAngle(Line(A,D),Triangle(A,B,C))], [BisectsAngle(Line(D,C),Triangle(A,B,C))] and [Equals(MeasureOf(Angle(B)),76)] [Find(MeasureOf(Angle(A,D,C)))]?"
"Find the perimeter of the \triangle DEF, if \triangle ABC \sim \triangle DEF, AB = 5, BC = 6, AC = 7, and DE = 3.","[Find(PerimeterOf(Triangle(D,E,F)))], if [Similar(Triangle(A,B,C),Triangle(D,E,F))], [Equals(LengthOf(Line(A,B)),5)] [Equals(LengthOf(Line(B,C)),6)] [Equals(LengthOf(Line(A,C)),7)] and [Equals(LengthOf(Line(D,E)),3)]."
Use parallelogram JKLM to find m \angle MJK.,"Use [Parallelogram(J,K,L,M)] to [Find(MeasureOf(Angle(M,J,K)))]."
Find the perimeter of \triangle ABC.,"[Find(PerimeterOf(Triangle(A,B,C)))]."
Find the area of the figure. Round to the nearest tenth.,[Find(AreaOf(Shape($)))]. Round to nearest tenth.
Find the base of the parallelogram given its area with 100 square units.,"[Find(BaseOf(Parallelogram($)))], [Equals(AreaOf(Parallelogram($)),100)]."
Find x.,[Find(x)].
Find m \angle G.,[Find(MeasureOf(Angle(G)))].
Find x.,[Find(x)].
Find x.,[Find(x)].
Find x in the figure.,[Find(x)].
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
Find x in the figure below. Round your answer to the nearest tenth if necessary.,[Find(x)]. Round to nearest tenth if necessary.
Find y.,[Find(y)].
The segment is tangent to the circle. Find x.,"[Tangent(Line($),Circle($))] to [Circle($)]. [Find(x)]."
Find y.,[Find(y)].
"Quadrilateral JKLM is a rectangle. If m \angle KJL = 2x+4 and m \angle JLK = 7x+5, find x."," [Rectangle(J,K,L,M)]. If [Equals(MeasureOf(Angle(K,J,L)),2x+4)] and [Equals(MeasureOf(Angle(J,L,K)),7x+5)] [Find(x)]."
"\triangle DFG and \triangle FGH are isosceles, m \angle FDH = 28 and DG \cong FG \cong FH. Find the measure of \angle GFH.","[Isosceles(Triangle(D,F,G))], [Isosceles(Triangle(F,G,H))], [Equals(MeasureOf(Angle(F,D,H)),28)] and [Equals(LengthOf(Line(D,G)),Line(F,G))], [Equals(LengthOf(Line(F,G)),Line(F,H))]. [Find(MeasureOf(Angle(G,F,H)))]."
find \cos B.,[Find(CosOf(Angle(B)))].
Each pair of polygons is similar. Find x.,"[Similar(Polygon($1),Polygon($2))]. [Find(x)]."
Use parallelogram PQRS to find m \angle R.,"Use [Parallelogram(P,Q,R,S)] to [Find(MeasureOf(Angle(R)))]."
\odot J \cong \odot K and \widehat MN \cong \widehat PQ. Find PQ.,"[Congruent(Circle(J),Circle(K))] and [Congruent(Arc(M,N),Arc(P,Q))]. [Find(LengthOf(Line(P,Q)))]."
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find m \angle 5.,[Find(MeasureOf(Angle(5)))].
Find the measure of \angle 4 if l \parallel m and m \angle 1 = 105.,"[Find(MeasureOf(Angle(4)))] if [Parallel(Line(l),Line(m))] and [Equals(MeasureOf(Angle(1)),105)]."
Find z.,[Find(z)].
\triangle NDG \cong \triangle LGD. Find x.,"[Congruent(Triangle(N,D,G),Triangle(L,G,D))]. [Find(x)]."
WXYZ is a parallelogram. Find m \angle XWZ.," [Parallelogram(W,X,Y,Z)]. [Find(MeasureOf(Angle(X,W,Z)))]."
Find RT.,"[Find(LengthOf(Line(R,T)))]."
Find x to the nearest tenth. ,[Find(x)] to nearest tenth.
Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. Round to nearest tenth if necessary. [Tangent(Line($),Circle($))]."
"If PR \parallel KL, KN = 9, LN = 16, PM = 2 KP, find ML.","If [Parallel(Line(P,R),Line(K,L))], [Equals(LengthOf(Line(K,N)),9)] [Equals(LengthOf(Line(L,N)),16)] [Equals(LengthOf(Line(P,M)),Mul(Line(K,P),2))], [Find(LengthOf(Line(M,L)))]."
Find m \angle C.,[Find(MeasureOf(Angle(C)))].
"If \frac{IJ}{XJ} = \frac{HJ}{YJ}, m \angle WXJ = 130 and m \angle WZG = 20, find m \angle JHI.","If [Equals(RatioOf(Line(I,J),Line(X,J)),RatioOf(Line(H,J),Line(Y,J)))], [Equals(MeasureOf(Angle(W,X,J)),130)] and [Equals(MeasureOf(Angle(W,Z,G)),20)] [Find(MeasureOf(Angle(J,H,I)))]."
"If EC is an altitude of \triangle AED, m \angle 1 = 2x+7, and m \angle 2 = 3x+13, find m \angle 2.","If [Equals(Line(E,C),AltitudeOf(Triangle(A,E,D)))], [Equals(MeasureOf(Angle(1)),2x+7)] and [Equals(MeasureOf(Angle(2)),3x+13)] [Find(MeasureOf(Angle(2)))]."
Find the perimeter of the figure.,[Find(PerimeterOf(Shape($)))].
Find x.,[Find(x)].
Find x so that m \parallel n.,"[Find(x)] so [Parallel(Line(m),Line(n))]."
"In \odot X, AB = 30, CD = 30, and m \widehat CZ = 40. Find CN.","In [Circle(X)], [Equals(LengthOf(Line(A,B)),30)] [Equals(LengthOf(Line(C,D)),30)] and [Equals(MeasureOf(Arc(C,Z)),40)] [Find(LengthOf(Line(C,N)))]."
"Points S, T, and U are the midpoints of DE, EF, and DF, respectively. Find z.","[IsMidpointOf(Point(S),Line(D,E))], [IsMidpointOf(Point(T),Line(E,F))], [IsMidpointOf(Point(U),Line(D,F))],,. [Find(z)]."
Find the area of the figure. Round to the nearest tenth.,[Find(AreaOf(Shape($)))]. Round to nearest tenth.
\triangle WXY and \triangle XYZ are isosceles and m \angle XYZ = 128. Find the measure of \angle WXY.,"[Isosceles(Triangle(W,X,Y))], [Isosceles(Triangle(X,Y,Z))] and [Equals(MeasureOf(Angle(X,Y,Z)),128)] [Find(MeasureOf(Angle(W,X,Y)))]."
Find the measure of \angle 6 if l \parallel m and m \angle 1 = 105.,"[Find(MeasureOf(Angle(6)))] if [Parallel(Line(l),Line(m))] and [Equals(MeasureOf(Angle(1)),105)]."
Express the ratio of \tan C as a decimal to the nearest hundredth.,[Find(RatioOf(TanOf(Angle(C))))] to nearest hundredth.
Find x.,[Find(x)].
Find x.,[Find(x)].
Find ST.,"[Find(LengthOf(Line(S,T)))]."
"In the figure, m \angle 9 = 75. Find the measure of \angle 5.",", [Equals(MeasureOf(Angle(9)),75)] [Find(MeasureOf(Angle(5)))]."
Find x.,[Find(x)].
Find x if \triangle JMN is an isosceles triangle with JM \cong MN.,"[Find(x)] if [Isosceles(Triangle(J,M,N))] with [Equals(LengthOf(Line(J,M)),Line(M,N))]."
Find the area of the figure.,[Find(AreaOf(Shape($)))].
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find the perimeter of \parallelogram ABCD.,"[Find(PerimeterOf(Parallelogram(A,B,C,D)))]."
"Assume that the segment is tangent, find the value of x.","[Tangent(Line($),Circle($))], [Find(x)]."
Find the area of the shaded region. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth.
Find x.,[Find(x)].
What is the total area of the figure?,[Find(AreaOf(Shape($)))]?
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
"Use parallelogram to, find x.",Use [Parallelogram($)] to [Find(x)].
Find m \angle 4.,[Find(MeasureOf(Angle(4)))].
Find m \angle H.,[Find(MeasureOf(Angle(H)))].
"Polygon ABCD \sim polygon AEFG, m \angle AGF = 108, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26. Find BC.","[Similar(Quadrilateral(A,B,C,D),Quadrilateral(A,E,F,G))], [Equals(MeasureOf(Angle(A,G,F)),108)] [Equals(LengthOf(Line(G,F)),14)] [Equals(LengthOf(Line(A,D)),12)] [Equals(LengthOf(Line(D,G)),4.5)] [Equals(LengthOf(Line(E,F)),8)] and [Equals(LengthOf(Line(A,B)),26)] [Find(LengthOf(Line(B,C)))]."
Find m \widehat CD.,"[Find(MeasureOf(Arc(C,D)))]."
Find YZ of isosceles \triangle XYZ.,"[Find(LengthOf(Line(Y,Z)))] of [Isosceles(Triangle(X,Y,Z))]."
Find AC.,"[Find(LengthOf(Line(A,C)))]."
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find m \angle W.,[Find(MeasureOf(Angle(W)))].
Find the area of the shaded region formed by the circle and regular polygon. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))] formed by [Circle($)] and [Regular(Polygon($))]. Round to nearest tenth.
"If PR \parallel KL, KN = 9, LN = 16, PM = 2 KP, find KM.","If [Parallel(Line(P,R),Line(K,L))], [Equals(LengthOf(Line(K,N)),9)] [Equals(LengthOf(Line(L,N)),16)] [Equals(LengthOf(Line(P,M)),Mul(Line(K,P),2))], [Find(LengthOf(Line(K,M)))]."
Find the perimeter of the triangle. Round to the nearest hundredth.,[Find(PerimeterOf(Triangle($)))]. Round to nearest hundredth.
"Triangle LMN is equilateral, and MP bisects LN. Find x.","[Equilateral(Triangle(L,M,N))] and [BisectsAngle(Line(M,P),Line(L,N))]. [Find(x)]."
Find x. A = 92 in^2.,"[Find(x)]. [Equals(AreaOf(Shape(A)),92)]."
Find b in the given parallelogram.,[Find(b)] in [Parallelogram($)].
"In \odot F, FH \cong FL and FK = 17. Find KM.","In [Circle(F)], [Equals(LengthOf(Line(F,H)),Line(F,L))] and [Equals(LengthOf(Line(F,K)),17)] [Find(LengthOf(Line(K,M)))]."
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find m \angle F.,[Find(MeasureOf(Angle(F)))].
Find m \angle C.,[Find(MeasureOf(Angle(C)))].
Quadrilateral WXYZ is a rectangle. Find the measure of \angle 12 if m \angle 1 = 30.," [Rectangle(W,X,Y,Z)]. [Find(MeasureOf(Angle(12)))] if [Equals(MeasureOf(Angle(1)),30)]."
Use parallelogram to find y.,Use [Parallelogram($)] to [Find(y)].
Find CB.,"[Find(LengthOf(Line(C,B)))]."
"JH, JP, and PH are midsegments of \triangle KLM. Find x.","[IsMidsegmentOf(Line(J,H),Triangle(K,L,M))], [IsMidsegmentOf(Line(J,P),Triangle(K,L,M))], [IsMidsegmentOf(Line(P,H),Triangle(K,L,M))],. [Find(x)]."
Find the area of the parallelogram.,[Find(AreaOf(Parallelogram($)))].
Find the area of \parallelogram TRVW.,"[Find(AreaOf(Parallelogram(T,R,V,W)))]."
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find the value of the variable x in the figure.,[Find(x)].
Express the ratio of \cos L as a decimal to the nearest hundredth.,[Find(RatioOf(CosOf(Angle(L))))] to nearest hundredth.
Find the area of the figure to the nearest tenth.,[Find(AreaOf(Shape($)))] to nearest tenth.
Find m \angle RSU so that m \parallel n.,"[Find(MeasureOf(Angle(R,S,U)))] so [Parallel(Line(m),Line(n))]."
"m \angle BAC = 40, m \angle DAC = 40, and DC = 10, find BC.","[Equals(MeasureOf(Angle(B,A,C)),40)] [Equals(MeasureOf(Angle(D,A,C)),40)] and [Equals(LengthOf(Line(D,C)),10)] [Find(LengthOf(Line(B,C)))]."
Find x.,[Find(x)].
Find the measure of \angle A to the nearest tenth.,[Find(MeasureOf(Angle(A)))] to nearest tenth.
"The diameters of \odot A, \odot B, and \odot C are 10, 30 and 10 units, respectively. Find BY if AZ \cong CW and CW = 2.","[Equals(DiameterOf(Circle(A)),10)] [Equals(DiameterOf(Circle(B)),30)] [Equals(DiameterOf(Circle(C)),10)] [Find(LengthOf(Line(B,Y)))] if [Equals(LengthOf(Line(A,Z)),Line(C,W))] and [Equals(LengthOf(Line(C,W)),2)]."
Find the area of the shaded region. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth.
Find z.,[Find(z)].
What is the value of x in the figure?,[Find(x)]?
Find m \angle DAB.,"[Find(MeasureOf(Angle(D,A,B)))]."
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
"If JL = 27, BL = 9, and JK = 18, find JA.","If [Equals(LengthOf(Line(J,L)),27)] [Equals(LengthOf(Line(B,L)),9)] and [Equals(LengthOf(Line(J,K)),18)] [Find(LengthOf(Line(J,A)))]."
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find x. Assume that any segment that appears to be tangent is tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
"Circle J has a radius of 10 units, \odot K has a radius of 8 units, and BC = 5.4 units. Find AB.","[Equals(RadiusOf(Circle(J)),10)] [Equals(RadiusOf(Circle(K)),8)] and [Equals(LengthOf(Line(B,C)),5.4)] [Find(LengthOf(Line(A,B)))]."
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
Find m \angle E.,[Find(MeasureOf(Angle(E)))].
What is the measure of \angle GHI?,"[Find(MeasureOf(Angle(G,H,I)))]?"
"Find the ratio of MS to SP, given that MNPQ is a parallelogram with MR = \frac{1}{4} MN.","[Find(RatioOf(Line(M,S),Line(S,P)))], [Parallelogram(M,N,P,Q)] with [Equals(LengthOf(Line(M,R)),Mul(Line(M,N),\frac{1}{4}))]."
"Find the measure of ST of equilateral triangle RST if RS = x+9, ST = 2x, and RT = 3x-9.","[Find(LengthOf(Line(S,T)))] of [Equilateral(Triangle(R,S,T))] if [Equals(LengthOf(Line(R,S)),x+9)] [Equals(LengthOf(Line(S,T)),2x)] and [Equals(LengthOf(Line(R,T)),3x-9)]."
Find x.,[Find(x)].
Find the area of the triangle. Round to the nearest hundredth.,[Find(AreaOf(Triangle($)))]. Round to nearest hundredth.
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
"In the figure, m \angle 1 = 50 and m \angle 3 = 60. Find the measure of \angle 2.",", [Equals(MeasureOf(Angle(1)),50)] and [Equals(MeasureOf(Angle(3)),60)] [Find(MeasureOf(Angle(2)))]."
Find the diameter of circle M.,[Find(DiameterOf(Circle(M)))].
Find m \angle 7.,[Find(MeasureOf(Angle(7)))].
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
Triangle RST is circumscribed about the circle below. What is the perimeter of the triangle?,"[CircumscribedTo(Triangle(R,S,T),Circle($))]. [Find(PerimeterOf(Triangle($)))]?"
Rhombus ABCD is circumscribed about \odot P and has a perimeter of 32. Find x.,"[CircumscribedTo(Rhombus(A,B,C,D),Circle(P))], [Equals(PerimeterOf(Rhombus(A,B,C,D)),32)] [Find(x)]."
Find m \widehat GJF.,"[Find(MeasureOf(Arc(G,J,F)))]."
"Find BC if BE = 24, CD = 32, and AB = 33.","[Find(LengthOf(Line(B,C)))] if [Equals(LengthOf(Line(B,E)),24)] [Equals(LengthOf(Line(C,D)),32)] and [Equals(LengthOf(Line(A,B)),33)]."
JH is a midsegment of \triangle KLM. Find x.,"[IsMidsegmentOf(Line(J,H),Triangle(K,L,M))]. [Find(x)]."
H is the incenter of \triangle ABC. Find m \angle DHG.,"[IsIncenterOf(Point(H),Triangle(A,B,C))]. [Find(MeasureOf(Angle(D,H,G)))]."
"Find EH if \triangle ABC \sim \triangle DEF, BG is an altitude of \triangle ABC, EH is an altitude of \triangle DEF, BG = 3, BF = 4, FC = 2, and CE = 1.","[Find(LengthOf(Line(E,H)))] if [Similar(Triangle(A,B,C),Triangle(D,E,F))], [Equals(Line(B,G),AltitudeOf(Triangle(A,B,C)))], [Equals(Line(E,H),AltitudeOf(Triangle(D,E,F)))], [Equals(LengthOf(Line(B,G)),3)] [Equals(LengthOf(Line(B,F)),4)] [Equals(LengthOf(Line(F,C)),2)] and [Equals(LengthOf(Line(C,E)),1)]."
"m \angle 19 = 100+20x, m \angle 20 = 20x. Find the measure of \angle 19.","[Equals(MeasureOf(Angle(19)),100+20x)] [Equals(MeasureOf(Angle(20)),20x)] [Find(MeasureOf(Angle(19)))]."
Find x.,[Find(x)].
"If AC = 14, BC = 8, and AD = 21, find ED.","If [Equals(LengthOf(Line(A,C)),14)] [Equals(LengthOf(Line(B,C)),8)] and [Equals(LengthOf(Line(A,D)),21)] [Find(LengthOf(Line(E,D)))]."
Find z.,[Find(z)].
"In the figure, m \angle 3 = 110 and m \angle 12 = 55. Find the measure of \angle 6.",", [Equals(MeasureOf(Angle(3)),110)] and [Equals(MeasureOf(Angle(12)),55)] [Find(MeasureOf(Angle(6)))]."
RP = 3.5 and JP = 9. Find PL.,"[Equals(LengthOf(Line(R,P)),3.5)] and [Equals(LengthOf(Line(J,P)),9)] [Find(LengthOf(Line(P,L)))]."
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find the measure of \angle 1.,[Find(MeasureOf(Angle(1)))].
"In the figure, the vertices of quadrilateral ABCD intersect square EFGH and divide its sides into segments with measure that have a ratio of 1:2. Find the area of ABCD.",", vertices of [Quadrilateral(A,B,C,D)] intersect [Square(E,F,G,H)] and divide sides into segments with measure have a ratio of 1:2. [Find(AreaOf(Quadrilateral(A,B,C,D)))]."
H is the incenter of \triangle ABC. Find BD.,"[IsIncenterOf(Point(H),Triangle(A,B,C))]. [Find(LengthOf(Line(B,D)))]."
"Quadrilateral EFGH is a rectangle. If m \angle FEG = 57, find m \angle GEH."," [Rectangle(E,F,G,H)]. If [Equals(MeasureOf(Angle(F,E,G)),57)] [Find(MeasureOf(Angle(G,E,H)))]."
"For the pair of similar figures, use the given areas to find x.","[Similar(Shape($1),Shape($2))], to [Find(x)]."
Use parallelogram NQRM to find QR.,"Use [Parallelogram(N,Q,R,M)] to [Find(LengthOf(Line(Q,R)))]."
Find x.,[Find(x)].
What is the ratio of the measure of \angle ACB to the measure of \angle AOB?,"[Find(RatioOf(MeasureOf(Angle(A,C,B)),MeasureOf(Angle(A,O,B))))]?"
Quadrilateral ABCD is a rectangle. Find y.," [Rectangle(A,B,C,D)]. [Find(y)]."
Use parallelogram to find a.,Use [Parallelogram($)] to [Find(a)].
Find the perimeter of \triangle QRS if \triangle QRS \sim \triangle QTP.,"[Find(PerimeterOf(Triangle(Q,R,S)))] if [Similar(Triangle(Q,R,S),Triangle(Q,T,P))]."
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
Find the area of the sector. Round to the nearest tenth.,[Find(AreaOf(Sector($)))]. Round to nearest tenth.
Find the perimeter of the figure.,[Find(PerimeterOf(Shape($)))].
Find BC.,"[Find(LengthOf(Line(B,C)))]."
Find \angle W.,[Find(MeasureOf(Angle(W)))].
Find y.,[Find(y)].
"Find the perimeter of the polygon for the given information. ST = 18, radius of \odot P = 5.","[Find(PerimeterOf(Polygon($)))] for. [Equals(LengthOf(Line(S,T)),18)] [Equals(RadiusOf(Circle(P)),5)]."
Find x. Assume that any segment that appears to be tangent is tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
"In \odot D, DE \cong EC, m CF = 60, and DE \perp EC. Find m \angle 4.","In [Circle(D)], [Equals(LengthOf(Line(D,E)),Line(E,C))], [Equals(LengthOf(Line(C,F)),60)] and [Perpendicular(Line(D,E),Line(E,C))]. [Find(MeasureOf(Angle(4)))]."
Find the area of the triangle. Round to the nearest tenth if necessary.,[Find(AreaOf(Triangle($)))]. Round to nearest tenth if necessary.
"In the figure, GK \cong GH and HK \cong KJ. If m \angle HGK = 42, find m \angle HJK.",", [Equals(LengthOf(Line(G,K)),Line(G,H))] and [Equals(LengthOf(Line(H,K)),Line(K,J))]. If [Equals(MeasureOf(Angle(H,G,K)),42)] [Find(MeasureOf(Angle(H,J,K)))]."
Find the area of the regular polygon figure. Round to the nearest tenth.,[Find(AreaOf(Regular(Polygon($))))]. Round to nearest tenth.
"If PT = y-3, PS = y+2, RS = 12, and QS = 16 solve for y.","If [Equals(LengthOf(Line(P,T)),y-3)] [Equals(LengthOf(Line(P,S)),y+2)] [Equals(LengthOf(Line(R,S)),12)] and [Equals(LengthOf(Line(Q,S)),16)] [Find(y)]."
Find AB.,"[Find(LengthOf(Line(A,B)))]."
"In the figure, m \angle 3 = 43. Find the measure of \angle 7.",", [Equals(MeasureOf(Angle(3)),43)] [Find(MeasureOf(Angle(7)))]."
Find y.,[Find(y)].
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
"In the figure, a \parallel b, c \parallel d, and m \angle 4 = 57. Find the measure of \angle 10.",", [Parallel(Line(a),Line(b))], [Parallel(Line(c),Line(d))] and [Equals(MeasureOf(Angle(4)),57)] [Find(MeasureOf(Angle(10)))]."
"UJ = 9, VJ = 3, and ZT = 18. Find YJ.","[Equals(LengthOf(Line(U,J)),9)] [Equals(LengthOf(Line(V,J)),3)] and [Equals(LengthOf(Line(Z,T)),18)] [Find(LengthOf(Line(Y,J)))]."
Find the measure of \angle 3.,[Find(MeasureOf(Angle(3)))].
Find x.,[Find(x)].
"If ABCDE \sim PQRST, find the perimeter of PQRST.","If [Similar(Pentagon(A,B,C,D,E),Pentagon(P,Q,R,S,T))], [Find(PerimeterOf(Pentagon(P,Q,R,S,T)))]."
"If KH is parallel to JI, find the measure of \angle 3.","If [Parallel(Line(K,H),Line(J,I))], [Find(MeasureOf(Angle(3)))]."
"In rhombus LMPQ, m \angle QLM = 2x^{2}-10, m \angle QPM = 8x, and MP = 10. Find QL.","In [Rhombus(L,M,P,Q)], [Equals(MeasureOf(Angle(Q,L,M)),2x^{2}-10)] [Equals(MeasureOf(Angle(Q,P,M)),8x)] and [Equals(LengthOf(Line(M,P)),10)] [Find(LengthOf(Line(Q,L)))]."
Find DF.,"[Find(LengthOf(Line(D,F)))]."
Use parallelogram ABCD to find m \angle FBC.,"Use [Parallelogram(A,B,C,D)] to [Find(MeasureOf(Angle(F,B,C)))]."
Find the measure of \angle T to the nearest tenth.,[Find(MeasureOf(Angle(T)))] to nearest tenth.
"If c = 8, find b.","If [Equals(c,8)] [Find(b)]."
Find x and so that the quadrilateral is a parallelogram.,[Find(x)] and so [Parallelogram($)]
Find x.,[Find(x)].
"If x = 7\sqrt{3}, find a.","If [Equals(x,7\sqrt{3})] [Find(a)]."
Find y in the parallelogram.,[Find(y)] in [Parallelogram($)].
Find m \angle Z.,[Find(MeasureOf(Angle(Z)))].
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
Find x. Round the angle measure to the nearest degree.,[Find(x)]. Round angle measure to nearest degree.
Use parallelogram to find y.,Use [Parallelogram($)] to [Find(y)].
Find m \angle A.,[Find(MeasureOf(Angle(A)))].
Find the measure of the altitude drawn to the hypotenuse.,"[Find(LengthOf(AltitudeOf(Triangle($1,$2,$3))))], [IsHypotenuseOf(Line($1,$3),Triangle($1,$2,$3))]."
"In the figure, a regular polygon is inscribed in a circle. Find the measure of a central angle.",", [InscribedIn(Regular(Polygon($)),Circle($))]. [Find(MeasureOf(Angle($)))]."
Find x.,[Find(x)].
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
"\angle 6 and \angle 8 are complementary, m \angle 8 = 47. Find the measure of \angle 6.","[Equals(SumOf(MeasureOf(Angle(6)),MeasureOf(Angle(6))),90)], [Equals(MeasureOf(Angle(8)),47)] [Find(MeasureOf(Angle(6)))]."
"The two polygons are similar. Then, find y.","two [Similar(Polygon($1),Polygon($2))]. Then, [Find(y)]."
Find x.,[Find(x)].
Find x.,[Find(x)].
Find x.,[Find(x)].
The area of a circle is 20\pi square centimeters. What is its circumference?,"[Equals(AreaOf(Circle($)),20\pi)] [Find(CircumferenceOf(Circle($)))]?"
Find m \widehat PM.,"[Find(MeasureOf(Arc(P,M)))]."
PQ is tangent to the circle. Find x. Round to the nearest tenth.,"[Tangent(Line(P,Q),Circle($))]. [Find(x)]. Round to nearest tenth."
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
"In the figure, below, square ABCD is attached to \triangle ADE as shown. If m \angle EAD is 30 and AE is equal to 4\sqrt{3}, then what is the area of square ABCD?",",, [Square(A,B,C,D)] is attached to [Triangle(A,D,E)]. If [Equals(MeasureOf(Angle(E,A,D)),30)] and [Equals(LengthOf(Line(A,E)),4\sqrt{3})] [Find(AreaOf(Square(A,B,C,D)))]?"
Find the area of the trapezoid.,[Find(AreaOf(Trapezoid($)))].
Find x.,[Find(x)].
"Find the perimeter of the \triangle CBH, if \triangle CBH \sim \triangle FEH, ADEG is a parallelogram, CH = 7, FH = 10, FE = 11, and EH = 6. Rounded to the nearest tenth.","[Find(PerimeterOf(Triangle(C,B,H)))], if [Similar(Triangle(C,B,H),Triangle(F,E,H))], [Parallelogram(A,D,E,G)], [Equals(LengthOf(Line(C,H)),7)] [Equals(LengthOf(Line(F,H)),10)] [Equals(LengthOf(Line(F,E)),11)] and [Equals(LengthOf(Line(E,H)),6)] Rounded to nearest tenth."
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
"Find RS if PQ = 12, QR = 2, and TS = 3.","[Find(LengthOf(Line(R,S)))] if [Equals(LengthOf(Line(P,Q)),12)] [Equals(LengthOf(Line(Q,R)),2)] and [Equals(LengthOf(Line(T,S)),3)]."
"isosceles trapezoid TWYZ with \angle Z \cong \angle Y, m \angle Z = 30x, \angle T \cong \angle W, and m \angle T = 20x, find \angle T.","[Isosceles(Trapezoid(T,W,Y,Z))] with [Equals(Angle(Z),Angle(Y))], [Equals(MeasureOf(Angle(Z)),30x)] [Equals(Angle(T),Angle(W))] and [Equals(MeasureOf(Angle(T)),20x)] [Find(MeasureOf(Angle(T)))]."
"If AB and JK are altitudes, \triangle DAC \sim \triangle MJL, AB = 9, AD = 4x-8, JK = 21, and JM = 5x+3, find x.","If [IsAltitudeOf(Line(A,B),Shape($))], [IsAltitudeOf(Line(J,K),Shape($))], [Similar(Triangle(D,A,C),Triangle(M,J,L))], [Equals(LengthOf(Line(A,B)),9)] [Equals(LengthOf(Line(A,D)),4x-8)] [Equals(LengthOf(Line(J,K)),21)] and [Equals(LengthOf(Line(J,M)),5x+3)] [Find(x)]."
What is the circumference of \odot T? Round to the nearest tenth.,[Find(CircumferenceOf(Circle(T)))]? Round to nearest tenth.
Find the length of \widehat ZY. Round to the nearest hundredth.,"[Find(LengthOf(Arc(Z,Y)))]. Round to nearest hundredth."
Find x.,[Find(x)].
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Find m \widehat AC.,"[Find(MeasureOf(Arc(A,C)))]."
"If CDFG is a kite, find m \angle D.","If [Kite(C,D,F,G)], [Find(MeasureOf(Angle(D)))]."
Find RT.,"[Find(LengthOf(Line(R,T)))]."
Use parallelogram NQRM to find x.,"Use [Parallelogram(N,Q,R,M)] to [Find(x)]."
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
"BC \parallel DF. AC = 15, BD = 3x-2, CF = 3x+2, and AB = 12. Find x.","[Parallel(Line(B,C),Line(D,F))]. [Equals(LengthOf(Line(A,C)),15)] [Equals(LengthOf(Line(B,D)),3x-2)] [Equals(LengthOf(Line(C,F)),3x+2)] and [Equals(LengthOf(Line(A,B)),12)] [Find(x)]."
"For the pair of similar figures, use the given areas to find x.","[Similar(Shape($1),Shape($2))], to [Find(x)]."
Find y.,[Find(y)].
Find the area of the shaded region. Round to the nearest tenth if necessary.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth if necessary.
Quadrilateral ABDC is a rectangle. Find m \angle 5 if m \angle 1 = 38.," [Rectangle(A,B,D,C)]. [Find(MeasureOf(Angle(5)))] if [Equals(MeasureOf(Angle(1)),38)]."
Find the measure of m \widehat GH.,"[Find(MeasureOf(Arc(G,H)))]."
"In \triangle JLP, m \angle JMP = 3x-6, JK = 3y-2, and LK = 5y-8. If JM is an altitude of \triangle JLP, find x.","In [Triangle(J,L,P)], [Equals(MeasureOf(Angle(J,M,P)),3x-6)] [Equals(LengthOf(Line(J,K)),3y-2)] and [Equals(LengthOf(Line(L,K)),5y-8)] If [Equals(Line(J,M),AltitudeOf(Triangle(J,L,P)))], [Find(x)]."
Find m \angle Z.,[Find(MeasureOf(Angle(Z)))].
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Find x. Round the angle measure to the nearest degree.,[Find(x)]. Round angle measure to nearest degree.
P is the incenter of \angle XYZ. Find m \angle LZP.,"[IsIncenterOf(Point(P),Angle(X,Y,Z))]. [Find(MeasureOf(Angle(L,Z,P)))]."
"In quadrilateral PQRS, PQ = 721, QR = 547, RS = 593, PS = 756, and m \angle P = 58. Find m \angle R.","In [Quadrilateral(P,Q,R,S)], [Equals(LengthOf(Line(P,Q)),721)] [Equals(LengthOf(Line(Q,R)),547)] [Equals(LengthOf(Line(R,S)),593)] [Equals(LengthOf(Line(P,S)),756)] and [Equals(MeasureOf(Angle(P)),58)] [Find(MeasureOf(Angle(R)))]."
RP = 3.5 and JP = 9. Find PS.,"[Equals(LengthOf(Line(R,P)),3.5)] and [Equals(LengthOf(Line(J,P)),9)] [Find(LengthOf(Line(P,S)))]."
"In \odot Z, PZ = ZQ, XY = 4a-5, and ST =-5a+13. Find SQ.","In [Circle(Z)], [Equals(LengthOf(Line(P,Z)),Line(Z,Q))], [Equals(LengthOf(Line(X,Y)),4a-5)] and [Equals(LengthOf(Line(S,T)),-5a+13)] [Find(LengthOf(Line(S,Q)))]."
Find h.,[Find(h)].
Find the area of the sector. Round to the nearest tenth.,[Find(AreaOf(Sector($)))]. Round to nearest tenth.
Find y.,[Find(y)].
"For isosceles trapezoid ABCD, X and Y are midpoints of the legs. Find m \angle XBC if m \angle ADY = 78.","[Isosceles(Trapezoid(A,B,C,D))], [IsMidpointOf(Point(X),LegOf(Isosceles(Trapezoid(A,B,C,D))))], [IsMidpointOf(Point(Y),LegOf(Isosceles(Trapezoid(A,B,C,D))))],. [Find(MeasureOf(Angle(X,B,C)))] if [Equals(MeasureOf(Angle(A,D,Y)),78)]."
What is the perimeter of the figure?,[Find(PerimeterOf(Shape($)))]?
m \widehat JH = 114. Find m \angle 1.,"[Equals(MeasureOf(Arc(J,H)),114)] [Find(MeasureOf(Angle(1)))]."
Find x.,[Find(x)].
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
Find the area of the blue region.,[Find(AreaOf(Blue(Shape($))))].
What is the area of rectangle WXYZ?,"[Find(AreaOf(Rectangle(W,X,Y,Z)))]?"
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
Find YZ.,"[Find(LengthOf(Line(Y,Z)))]."
"Rhombus QRST has an area of 137.9 square meters. If RT is 12.2 meters, find QS.","[Equals(AreaOf(Rhombus(Q,R,S,T)),137.9)] If [Equals(Line(R,T),12.2)] [Find(LengthOf(Line(Q,S)))]."
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find x. Assume that any segment that appears to be tangent is tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Solve for x.,[Find(x)].
Find x.,[Find(x)].
"If AD = 8, AE = 12, and EC = 18, find AB.","If [Equals(LengthOf(Line(A,D)),8)] [Equals(LengthOf(Line(A,E)),12)] and [Equals(LengthOf(Line(E,C)),18)] [Find(LengthOf(Line(A,B)))]."
"In \odot S, m \angle TSR = 42. Find m \widehat KT.","In [Circle(S)], [Equals(MeasureOf(Angle(T,S,R)),42)] [Find(MeasureOf(Arc(K,T)))]."
Find the measure of m \angle C.,[Find(MeasureOf(Angle(C)))].
Find x.,[Find(x)].
"In \odot R, SU = 20, YW = 20, and m \widehat YX = 45. Find m \widehat ST.","In [Circle(R)], [Equals(LengthOf(Line(S,U)),20)] [Equals(LengthOf(Line(Y,W)),20)] and [Equals(MeasureOf(Arc(Y,X)),45)] [Find(MeasureOf(Arc(S,T)))]."
Find m \angle C.,[Find(MeasureOf(Angle(C)))].
Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. Round to nearest tenth if necessary. [Tangent(Line($),Circle($))]."
Find x.,[Find(x)].
Find DE.,"[Find(LengthOf(Line(D,E)))]."
Find m \angle W.,[Find(MeasureOf(Angle(W)))].
EC and AB are diameters of \odot O. Find its measure of \widehat ACB.,"[IsDiameterOf(Line(E,C),Circle(O))], [IsDiameterOf(Line(A,B),Circle(O))]. [Find(MeasureOf(Arc(A,C,B)))]."
Find the variable of b to the nearest tenth. Assume that segments that appear to be tangent are tangent.,"[Find(b)] to nearest tenth. [Tangent(Line($),Circle($))]."
Find the area of the figure. Round to the nearest tenth.,[Find(AreaOf(Shape($)))]. Round to nearest tenth.
Express the ratio of \tan X as a decimal to the nearest hundredth.,[Find(RatioOf(TanOf(Angle(X))))] to nearest hundredth.
Find x.,[Find(x)].
Find y.,[Find(y)].
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
J is the incenter of \angle ABC. Find JF.,"[IsIncenterOf(Point(J),Angle(A,B,C))]. [Find(LengthOf(Line(J,F)))]."
Find \angle 1.,[Find(MeasureOf(Angle(1)))].
Find the measure of \angle P.,[Find(MeasureOf(Angle(P)))].
Find the measure of the altitude drawn to the hypotenuse.,"[Find(LengthOf(AltitudeOf(Triangle($1,$2,$3))))], [IsHypotenuseOf(Line($1,$3),Triangle($1,$2,$3))]."
Find x.,[Find(x)].
Find y.,[Find(y)].
ABCD \sim QSRP. Find x.,"[Similar(Quadrilateral(A,B,C,D),Quadrilateral(Q,S,R,P))]. [Find(x)]."
"If WP is a perpendicular bisector, m \angle WHA = 8q+17, m \angle HWP = 10+q, AP = 6r+4, and PH = 22+3r, find m \angle HWP.","If [IsPerpendicularBisectorOf(Line(W,P),Line($))], [Equals(MeasureOf(Angle(W,H,A)),8q+17)] [Equals(MeasureOf(Angle(H,W,P)),10+q)] [Equals(LengthOf(Line(A,P)),6r+4)] and [Equals(LengthOf(Line(P,H)),22+3r)] [Find(MeasureOf(Angle(H,W,P)))]."
Find KL.,"[Find(LengthOf(Line(K,L)))]."
Find x.,[Find(x)].
The segment is tangent to the circle. Find x.,"[Tangent(Line($),Circle($))] to [Circle($)]. [Find(x)]."
"In the figure, a \parallel b, c \parallel d, and m \angle 4 = 57. Find the measure of \angle 8.",", [Parallel(Line(a),Line(b))], [Parallel(Line(c),Line(d))] and [Equals(MeasureOf(Angle(4)),57)] [Find(MeasureOf(Angle(8)))]."
Find x.,[Find(x)].
Find x.,[Find(x)].
Find x.,[Find(x)].
Use parallelogram to find x.,Use [Parallelogram($)] to [Find(x)].
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find y.,[Find(y)].
Find the area of the kite.,[Find(AreaOf(Kite($)))].
Find x to the nearest tenth.,[Find(x)] to nearest tenth.
Triangle ADC is circumscribed about \odot O. Find the perimeter of \triangle ADC if EC = DE+AF.,"[CircumscribedTo(Triangle(A,D,C),Circle(O))]. [Find(PerimeterOf(Triangle(A,D,C)))] if [Equals(LengthOf(Line(E,C)),Add(Line(D,E),Line(A,F)))]."
Find m \angle 4.,[Find(MeasureOf(Angle(4)))].
"For trapezoid DEGH, X and Y are midpoints of the legs. Find DE.","[Trapezoid(D,E,G,H)], [IsMidpointOf(Point(X),LegOf(Trapezoid(D,E,G,H)))], [IsMidpointOf(Point(Y),LegOf(Trapezoid(D,E,G,H)))],. [Find(LengthOf(Line(D,E)))]."
Find the area of the trapezoid.,[Find(AreaOf(Trapezoid($)))].
Find x.,[Find(x)].
"For trapezoid QRST, M and P are midpoints of the legs. If PM = 2x, QR = 3x, and TS = 10, find PM.","[Trapezoid(Q,R,S,T)], [IsMidpointOf(Point(M),LegOf(Trapezoid(Q,R,S,T)))], [IsMidpointOf(Point(P),LegOf(Trapezoid(Q,R,S,T)))],. If [Equals(LengthOf(Line(P,M)),2x)] [Equals(LengthOf(Line(Q,R)),3x)] and [Equals(LengthOf(Line(T,S)),10)] [Find(LengthOf(Line(P,M)))]."
Find the measure of \angle Z to the nearest tenth.,[Find(MeasureOf(Angle(Z)))] to nearest tenth.
Find m \angle K.,[Find(MeasureOf(Angle(K)))].
Find the value of h.,[Find(h)].
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find the perimeter of the figure.,[Find(PerimeterOf(Shape($)))].
Find the length of AB in the isosceles triangle ABC.,"[Find(LengthOf(Line(A,B)))] in [Isosceles(Triangle(A,B,C))]."
"In parallelogram ABCD, BD and AC intersect at E. If AE = 9, BE = 3x-7, and DE = x+5, find x.","In [IntersectAt(Parallelogram(A,B,C,D),Line(B,D),Line(A,C),Point(E))]. If [Equals(LengthOf(Line(A,E)),9)] [Equals(LengthOf(Line(B,E)),3x-7)] and [Equals(LengthOf(Line(D,E)),x+5)] [Find(x)]."
"Use rhombus ABCD with m \angle 1 = 2x+20, m \angle 2 = 5x-4, AC = 15, and m \angle 3 = y^{2}+26. Find x.","Use [Rhombus(A,B,C,D)] with [Equals(MeasureOf(Angle(1)),2x+20)] [Equals(MeasureOf(Angle(2)),5x-4)] [Equals(LengthOf(Line(A,C)),15)] and [Equals(MeasureOf(Angle(3)),y^{2}+26)] [Find(x)]."
Find VW.,"[Find(LengthOf(Line(V,W)))]."
Find the radius of \odot K. Round to the nearest hundredth.,[Find(RadiusOf(Circle(K)))]. Round to nearest hundredth.
Find the measure of XT.,"[Find(LengthOf(Line(X,T)))]."
Find m \angle Q.,[Find(MeasureOf(Angle(Q)))].
\triangle FGH is an equilateral triangle. Find HG.,"[Equilateral(Triangle(F,G,H))] [Triangle($)]. [Find(LengthOf(Line(H,G)))]."
Find x. Assume that any segment that appears to be tangent is tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
"AB is a diameter, AC = 8 inches, and BC = 15 inches. Find the diameter of the circle.","[IsDiameterOf(Line(A,B),Circle($))], [Equals(LengthOf(Line(A,C)),8)] and [Equals(LengthOf(Line(B,C)),15)] [Find(DiameterOf(Circle($)))]."
Find y in the given parallelogram.,[Find(y)] in [Parallelogram($)].
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
"Find m \widehat EDB if m \widehat FE = 118, m \widehat AB = 108, m \angle EGB = 52, and m \angle EFB = 30.","[Find(MeasureOf(Arc(E,D,B)))] if [Equals(MeasureOf(Arc(F,E)),118)] [Equals(MeasureOf(Arc(A,B)),108)] [Equals(MeasureOf(Angle(E,G,B)),52)] and [Equals(MeasureOf(Angle(E,F,B)),30)]."
"In \odot R, SU = 20, YW = 20, and m \widehat YX = 45. Find m \widehat SU.","In [Circle(R)], [Equals(LengthOf(Line(S,U)),20)] [Equals(LengthOf(Line(Y,W)),20)] and [Equals(MeasureOf(Arc(Y,X)),45)] [Find(MeasureOf(Arc(S,U)))]."
Find x.,[Find(x)].
Find x.,[Find(x)].
Find the measure of \angle 2 if m \angle DGF = 53 and m \angle AGC = 40.,"[Find(MeasureOf(Angle(2)))] if [Equals(MeasureOf(Angle(D,G,F)),53)] and [Equals(MeasureOf(Angle(A,G,C)),40)]."
"If RQ \cong RS and m \angle RQS = 75, find m \angle R.","If [Equals(LengthOf(Line(R,Q)),Line(R,S))] and [Equals(MeasureOf(Angle(R,Q,S)),75)] [Find(MeasureOf(Angle(R)))]."
Find x. Round to the nearest tenth if necessary.,[Find(x)]. Round to nearest tenth if necessary.
RS bisects \angle VRU. Solve for x.,"[BisectsAngle(Line(R,S),Angle(V,R,U))]. [Find(x)]."
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find the area of the shaded region.,[Find(AreaOf(Shaded(Shape($))))].
Find m \angle T.,[Find(MeasureOf(Angle(T)))].
Find m \angle AGD.,"[Find(MeasureOf(Angle(A,G,D)))]."
HK and IG are diameters of \odot L. Find m \widehat HGK.,"[IsDiameterOf(Line(H,K),Circle(L))], [IsDiameterOf(Line(I,G),Circle(L))]. [Find(MeasureOf(Arc(H,G,K)))]."
"In the figure, m \angle 11 = 62 and m \angle 14 = 38. Find the measure of \angle 6.",", [Equals(MeasureOf(Angle(11)),62)] and [Equals(MeasureOf(Angle(14)),38)] [Find(MeasureOf(Angle(6)))]."
m \widehat JH = 114. Find m \angle 3.,"[Equals(MeasureOf(Arc(J,H)),114)] [Find(MeasureOf(Angle(3)))]."
If QRST is a parallelogram. Find z.,"If [Parallelogram(Q,R,S,T)]. [Find(z)]."
Use parallelogram JKLM to find m \angle JML if JK = 2b+3 and JM = 3a.,"Use [Parallelogram(J,K,L,M)] to [Find(MeasureOf(Angle(J,M,L)))] if [Equals(LengthOf(Line(J,K)),2b+3)] and [Equals(LengthOf(Line(J,M)),3a)]."
"In \odot F, m \angle DFA = 50 and CF \perp FB. Find m \widehat CBE.","In [Circle(F)], [Equals(MeasureOf(Angle(D,F,A)),50)] and [Perpendicular(Line(C,F),Line(F,B))]. [Find(MeasureOf(Arc(C,B,E)))]."
Polygon BCDE \cong polygon RSTU. Find z.,"[Congruent(Quadrilateral(B,C,D,E),Quadrilateral(R,S,T,U))]. [Find(z)]."
"If m \angle ZYW = 2x-7 and m \angle WYX = 2x+5, find m \angle ZYW.","If [Equals(MeasureOf(Angle(Z,Y,W)),2x-7)] and [Equals(MeasureOf(Angle(W,Y,X)),2x+5)] [Find(MeasureOf(Angle(Z,Y,W)))]."
Find the area of the figure. Round to the nearest tenth.,[Find(AreaOf(Shape($)))]. Round to nearest tenth.
Find x.,[Find(x)].
Find x.,[Find(x)].
Find m \angle C.,[Find(MeasureOf(Angle(C)))].
Find x.,[Find(x)].
Find the perimeter of the figure. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Shape($)))]. Round to nearest tenth if necessary.
"In the figure, m \angle 11 = 62 and m \angle 14 = 38. Find the measure of \angle 3.",", [Equals(MeasureOf(Angle(11)),62)] and [Equals(MeasureOf(Angle(14)),38)] [Find(MeasureOf(Angle(3)))]."
What is the value of x below to the nearest tenth?,[Find(x)] to nearest tenth?
Find the circumference of the figure. Round to the nearest tenth.,[Find(CircumferenceOf(Shape($)))]. Round to nearest tenth.
"If NQ and VX are medians, \triangle PNR \sim \triangle WVY, NQ = 8, PR = 12, WY = 7x-1, and VX = 4x+2, find x.","If [IsMedianOf(Line(N,Q),Shape($))], [IsMedianOf(Line(V,X),Shape($))], [Similar(Triangle(P,N,R),Triangle(W,V,Y))], [Equals(LengthOf(Line(N,Q)),8)] [Equals(LengthOf(Line(P,R)),12)] [Equals(LengthOf(Line(W,Y)),7x-1)] and [Equals(LengthOf(Line(V,X)),4x+2)] [Find(x)]."
Find x.,[Find(x)].
"Find y. Round to the nearest tenth, if necessary.","[Find(y)]. Round to nearest tenth, if necessary."
Find the perimeter of ABCD.,"[Find(PerimeterOf(Quadrilateral(A,B,C,D)))]."
Express the ratio of \cos A as a decimal to the nearest hundredth.,[Find(RatioOf(CosOf(Angle(A))))] to nearest hundredth.
"If the perimeter of square 2 is 200 units and the perimeter of square 1 is 150 units, what is the perimeter of square 3?","If [Equals(PerimeterOf(Square(2)),200)] and [Equals(PerimeterOf(Square(1)),150)] [Find(PerimeterOf(Square(3)))]?"
"In rhombus LMPQ, m \angle QLM = 2x^{2}-10, m \angle QPM = 8x, and MP = 10. Find m \angle LQP.","In [Rhombus(L,M,P,Q)], [Equals(MeasureOf(Angle(Q,L,M)),2x^{2}-10)] [Equals(MeasureOf(Angle(Q,P,M)),8x)] and [Equals(LengthOf(Line(M,P)),10)] [Find(MeasureOf(Angle(L,Q,P)))]."
Find the length of \widehat AB. Round to the nearest hundredth.,"[Find(LengthOf(Arc(A,B)))]. Round to nearest hundredth."
Find y.,[Find(y)].
"If RQ \cong RS, RP \cong RT and m \angle RQS = 80, find m \angle P.","If [Equals(LengthOf(Line(R,Q)),Line(R,S))], [Equals(LengthOf(Line(R,P)),Line(R,T))] and [Equals(MeasureOf(Angle(R,Q,S)),80)] [Find(MeasureOf(Angle(P)))]."
The common chord AB between \odot P and \odot Q is perpendicular to the segment connecting the centers of the circles. If AB = 10 what is the length of PQ?,"common [IsChordOf(Line(A,B),Circle($))] between [Circle(P)] and [Perpendicular(Circle(Q),Line($))] connecting centers of circles. If [Equals(LengthOf(Line(A,B)),10)] [Find(LengthOf(Line(P,Q)))]?"
Find the perimeter of quadrilateral ABCD to the nearest tenth.,"[Find(PerimeterOf(Quadrilateral(A,B,C,D)))] to nearest tenth."
Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. Round to nearest tenth if necessary. [Tangent(Line($),Circle($))]."
Find x if \triangle QRS is an equilateral triangle.,"[Find(x)] if [Equilateral(Triangle(Q,R,S))] [Triangle($)]."
Find x. Assume that any segment that appears to be tangent is tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find x.,[Find(x)].
Find m \angle R.,[Find(MeasureOf(Angle(R)))].
"Use parallelogram to, find y.",Use [Parallelogram($)] to [Find(y)].
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find m \angle RCN.,"[Find(MeasureOf(Angle(R,C,N)))]."
Find x.,[Find(x)].
Find m \angle A.,[Find(MeasureOf(Angle(A)))].
"In the figure, \triangle ABC is isosceles, \triangle DCE is equilateral, and \triangle FCG is isosceles. Find the measure of the \angle 1 at vertex C.",", [Isosceles(Triangle(A,B,C))], [Equilateral(Triangle(D,C,E))] and [Isosceles(Triangle(F,C,G))]. [Find(MeasureOf(Angle(1)))], [Equals(Angle(1),Angle(C))]."
Find y.,[Find(y)].
"If JA = 25, AK = 10, and BL = 14, find JB.","If [Equals(LengthOf(Line(J,A)),25)] [Equals(LengthOf(Line(A,K)),10)] and [Equals(LengthOf(Line(B,L)),14)] [Find(LengthOf(Line(J,B)))]."
"In \odot P, PR = 15 and m \angle QPR = 120. Find the length of \widehat QR.","In [Circle(P)], [Equals(LengthOf(Line(P,R)),15)] and [Equals(MeasureOf(Angle(Q,P,R)),120)] [Find(LengthOf(Arc(Q,R)))]."
find \tan S.,[Find(TanOf(Angle(S)))].
Find y.,[Find(y)].
Find the measure of the altitude drawn to the hypotenuse.,"[Find(LengthOf(AltitudeOf(Triangle($1,$2,$3))))], [IsHypotenuseOf(Line($1,$3),Triangle($1,$2,$3))]."
"If BEFA \sim EDCB, find x.","If [Similar(Quadrilateral(B,E,F,A),Quadrilateral(E,D,C,B))], [Find(x)]."
Find x.,[Find(x)].
Find the measure of \angle 4 if m \angle DGF = 53 and m \angle AGC = 40.,"[Find(MeasureOf(Angle(4)))] if [Equals(MeasureOf(Angle(D,G,F)),53)] and [Equals(MeasureOf(Angle(A,G,C)),40)]."
Find DH.,"[Find(LengthOf(Line(D,H)))]."
Q is the incenter of \triangle JKL. Find QP.,"[IsIncenterOf(Point(Q),Triangle(J,K,L))]. [Find(LengthOf(Line(Q,P)))]."
Find x.,[Find(x)].
"In \odot P, JK = 10 and \widehat JKL = 134. Find PQ. Round to the nearest hundredth.","In [Circle(P)], [Equals(LengthOf(Line(J,K)),10)] and [Equals(Arc(J,K,L),134)] [Find(LengthOf(Line(P,Q)))]. Round to nearest hundredth."
Find WY.,"[Find(LengthOf(Line(W,Y)))]."
Find y.,[Find(y)].
Find z.,[Find(z)].
Find y. Round to the nearest tenth.,[Find(y)]. Round to nearest tenth.
Find x.,[Find(x)].
"WXYZ is a rhombus. If m \angle XYZ = 110, find m \angle ZWY."," [Rhombus(W,X,Y,Z)]. If [Equals(MeasureOf(Angle(X,Y,Z)),110)] [Find(MeasureOf(Angle(Z,W,Y)))]."
"UJ = 9, VJ = 3, and ZT = 18. Find YU.","[Equals(LengthOf(Line(U,J)),9)] [Equals(LengthOf(Line(V,J)),3)] and [Equals(LengthOf(Line(Z,T)),18)] [Find(LengthOf(Line(Y,U)))]."
Use parallelogram to find x.,Use [Parallelogram($)] to [Find(x)].
Find the perimeter of the triangle. Round to the nearest hundredth.,[Find(PerimeterOf(Triangle($)))]. Round to nearest hundredth.
"Polygon ABCD \sim polygon AEFG, m \angle AGF = 108, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26. Find the ratio of the perimeter of polygon ABCD to the perimeter of polygon AEFG.","[Similar(Quadrilateral(A,B,C,D),Quadrilateral(A,E,F,G))], [Equals(MeasureOf(Angle(A,G,F)),108)] [Equals(LengthOf(Line(G,F)),14)] [Equals(LengthOf(Line(A,D)),12)] [Equals(LengthOf(Line(D,G)),4.5)] [Equals(LengthOf(Line(E,F)),8)] and [Equals(LengthOf(Line(A,B)),26)] [Find(RatioOf(PerimeterOf(Quadrilateral(A,B,C,D)),PerimeterOf(Quadrilateral(A,E,F,G))))]."
Find m \widehat GH.,"[Find(MeasureOf(Arc(G,H)))]."
Find x.,[Find(x)].
Find x so that m \parallel n.,"[Find(x)] so [Parallel(Line(m),Line(n))]."
What is m \angle 1 in the figure below?,[Find(MeasureOf(Angle(1)))]?
Find the measure of \angle Q.,[Find(MeasureOf(Angle(Q)))].
The pair of polygons is similar. Find AG.,"[Similar(Polygon($1),Polygon($2))]. [Find(LengthOf(Line(A,G)))]."
Find the length of \widehat BC.,"[Find(LengthOf(Arc(B,C)))]."
"In \odot G, m \angle AGB = 30 and CG \perp GD. Find m \widehat FAB.","In [Circle(G)], [Equals(MeasureOf(Angle(A,G,B)),30)] and [Perpendicular(Line(C,G),Line(G,D))]. [Find(MeasureOf(Arc(F,A,B)))]."
Find z.,[Find(z)].
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. [Regular(Polygon($))]. Round to nearest tenth.
Find h.,[Find(h)].
Find x in the figure.,[Find(x)].
Find y.,[Find(y)].
"If AB = 8, KL = 10, and JB = 13, find JL.","If [Equals(LengthOf(Line(A,B)),8)] [Equals(LengthOf(Line(K,L)),10)] and [Equals(LengthOf(Line(J,B)),13)] [Find(LengthOf(Line(J,L)))]."
Find m \angle 8.,[Find(MeasureOf(Angle(8)))].
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
"In \odot P, PQ = 3, find m \widehat RTS. Round to the nearest hundredth.","In [Circle(P)], [Equals(LengthOf(Line(P,Q)),3)] [Find(MeasureOf(Arc(R,T,S)))]. Round to nearest hundredth."
RS is the midsegment of trapezoid MNOP. What is the length of RS?,"[IsMidsegmentOf(Line(R,S),Trapezoid(M,N,O,P))]. [Find(LengthOf(Line(R,S)))]?"
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find m \angle 4.,[Find(MeasureOf(Angle(4)))].
Find x.,[Find(x)].
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Find x.,[Find(x)].
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
"Find GK if GI = 14, GH = 7, and KJ = 6.","[Find(LengthOf(Line(G,K)))] if [Equals(LengthOf(Line(G,I)),14)] [Equals(LengthOf(Line(G,H)),7)] and [Equals(LengthOf(Line(K,J)),6)]."
Trapezoid PQRS has an area of 250 square inches. Find the height of PQRS.,"[Equals(AreaOf(Trapezoid(P,Q,R,S)),250)] [Find(HeightOf(Quadrilateral(P,Q,R,S)))]."
"TV is tangent to the circle, and R and S are points on the circle. What is the value of x to the nearest tenth?","[Tangent(Line(T,V),Circle($))] and R and S are points on [Circle($)]. [Find(x)] to nearest tenth?"
"QRST is a rectangle. If m \angle QTR = 2x^{2}-7 and m \angle SRT = x^{2}+18, find m \angle QTR."," [Rectangle(Q,R,S,T)]. If [Equals(MeasureOf(Angle(Q,T,R)),2x^{2}-7)] and [Equals(MeasureOf(Angle(S,R,T)),x^{2}+18)] [Find(MeasureOf(Angle(Q,T,R)))]."
\triangle WXY and \triangle XYZ are isosceles and m \angle XYZ = 128. Find the measure of \angle XWY.,"[Isosceles(Triangle(W,X,Y))], [Isosceles(Triangle(X,Y,Z))] and [Equals(MeasureOf(Angle(X,Y,Z)),128)] [Find(MeasureOf(Angle(X,W,Y)))]."
Find the measure of \angle Z to the nearest tenth.,[Find(MeasureOf(Angle(Z)))] to nearest tenth.
"For the pair of similar figures, use the given areas to find x.","[Similar(Shape($1),Shape($2))], to [Find(x)]."
"ABCD is a rectangle. If m \angle 1 = 12x+4 and m \angle 2 = 16x-12, find m \angle 2."," [Rectangle(A,B,C,D)]. If [Equals(MeasureOf(Angle(1)),12x+4)] and [Equals(MeasureOf(Angle(2)),16x-12)] [Find(MeasureOf(Angle(2)))]."
Find y.,[Find(y)].
"a = 8, b = 15, and c = 17, find \sin B.","[Equals(a,8)] [Equals(b,15)] and [Equals(c,17)] [Find(SinOf(Angle(B)))]."
Which polynomial best represents the area of the regular pentagon shown below?,[Find(AreaOf(Regular(Pentagon($))))]?
Find x.,[Find(x)].
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find the area of the regular polygon. Round to the nearest tenth.,[Find(AreaOf(Regular(Polygon($))))]. Round to nearest tenth.
Find z.,[Find(z)].
Find z.,[Find(z)].
Find x.,[Find(x)].
Which statement about the value of x is not true?,Which statement about x is not true?
Find x in the given parallelogram.,[Find(x)] in [Parallelogram($)].
Find x. A = 165 cm^2.,"[Find(x)]. [Equals(AreaOf(Shape(A)),165)]."
"If AB = 32 and FC = 11, find FE.","If [Equals(LengthOf(Line(A,B)),32)] and [Equals(LengthOf(Line(F,C)),11)] [Find(LengthOf(Line(F,E)))]."
Find the area of the shaded region. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth.
"In \odot F, m \angle DFA = 50 and CF \perp FB. Find m \widehat BE.","In [Circle(F)], [Equals(MeasureOf(Angle(D,F,A)),50)] and [Perpendicular(Line(C,F),Line(F,B))]. [Find(MeasureOf(Arc(B,E)))]."
"In \odot P, RT = 15, find the length of \widehat RS. Round to the nearest hundredth.","In [Circle(P)], [Equals(LengthOf(Line(R,T)),15)] [Find(LengthOf(Arc(R,S)))]. Round to nearest hundredth."
Find m \angle A.,[Find(MeasureOf(Angle(A)))].
Find x.,[Find(x)].
Find m \angle 3.,[Find(MeasureOf(Angle(3)))].
Find x. Round to the nearest tenth if necessary.,[Find(x)]. Round to nearest tenth if necessary.
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
Find the area of the shaded region. Assume the inscribed polygon is regular.,[Find(AreaOf(Shaded(Shape($))))]. Assume inscribed [Regular(Polygon($))].
Find x.,[Find(x)].
"AB, BC, CD, and AD are tangent to a circle. If AB = 19, BC = 6, and CD = 14, find AD.","[Tangent(Line(A,B),Circle($))], [Tangent(Line(B,C),Circle($))], [Tangent(Line(C,D),Circle($))], [Tangent(Line(A,D),Circle($))]. If [Equals(LengthOf(Line(A,B)),19)] [Equals(LengthOf(Line(B,C)),6)] and [Equals(LengthOf(Line(C,D)),14)] [Find(LengthOf(Line(A,D)))]."
"In \odot P, PD = 10, PQ = 10, and QE = 20, find AB.","In [Circle(P)], [Equals(LengthOf(Line(P,D)),10)] [Equals(LengthOf(Line(P,Q)),10)] and [Equals(LengthOf(Line(Q,E)),20)] [Find(LengthOf(Line(A,B)))]."
Find RS.,"[Find(LengthOf(Line(R,S)))]."
Find the measure of \angle 5.,[Find(MeasureOf(Angle(5)))].
Find y.,[Find(y)].
Find the measure of \angle 1 in the figure.,[Find(MeasureOf(Angle(1)))].
"In the figure, m \angle 4 = 104, m \angle 14 = 118. Find the measure of \angle 2.",", [Equals(MeasureOf(Angle(4)),104)] [Equals(MeasureOf(Angle(14)),118)] [Find(MeasureOf(Angle(2)))]."
Use parallelogram ABCD to find m \angle BCD.,"Use [Parallelogram(A,B,C,D)] to [Find(MeasureOf(Angle(B,C,D)))]."
Find m \widehat AC.,"[Find(MeasureOf(Arc(A,C)))]."
Find the measure of \angle 1.,[Find(MeasureOf(Angle(1)))].
"In \triangle GHJ, HP = 5x-16, PJ = 3x+8, m \angle GJN = 6y-3, m \angle NJH = 4y+23 and m \angle HMG = 4z+14. GP is a median of \triangle GHJ. Find HJ.","In [Triangle(G,H,J)], [Equals(LengthOf(Line(H,P)),5x-16)] [Equals(LengthOf(Line(P,J)),3x+8)] [Equals(MeasureOf(Angle(G,J,N)),6y-3)] [Equals(MeasureOf(Angle(N,J,H)),4y+23)] and [Equals(MeasureOf(Angle(H,M,G)),4z+14)] [IsMedianOf(Line(G,P),Triangle(G,H,J))]. [Find(LengthOf(Line(H,J)))]."
"In \odot F, if CF = 14 inches, what is the diameter of the circle?","In [Circle(F)], if [Equals(LengthOf(Line(C,F)),14)] [Find(DiameterOf(Circle($)))]?"
Find the area of the figure.,[Find(AreaOf(Shape($)))].
Find y.,[Find(y)].
Find the value of the variable y in the figure.,[Find(y)].
Find x.,[Find(x)].
Find JK.,"[Find(LengthOf(Line(J,K)))]."
Find the area of the shaded sector. Round to the nearest tenth.,[Find(AreaOf(Shaded(Sector($))))]. Round to nearest tenth.
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
"The diameters of \odot A, \odot B, and \odot C are 10 inches, 20 inches, and 14 inches, respectively. Find XB.","[Equals(DiameterOf(Circle(A)),10)] [Equals(DiameterOf(Circle(B)),20)] [Equals(DiameterOf(Circle(C)),14)] [Find(LengthOf(Line(X,B)))]."
Find x.,[Find(x)].
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
"Find the area of the figure. Round to the nearest tenth, if necessary.","[Find(AreaOf(Shape($)))]. Round to nearest tenth, if necessary."
"If PR \parallel WX, WX = 10, XY = 6, WY = 8, RY = 5, and PS = 3, find PY.","If [Parallel(Line(P,R),Line(W,X))], [Equals(LengthOf(Line(W,X)),10)] [Equals(LengthOf(Line(X,Y)),6)] [Equals(LengthOf(Line(W,Y)),8)] [Equals(LengthOf(Line(R,Y)),5)] and [Equals(LengthOf(Line(P,S)),3)] [Find(LengthOf(Line(P,Y)))]."
Find x.,[Find(x)].
"In \odot Z, \angle WZX \cong \angle XZY, m \angle VZU = 4x, m \angle UZY = 2x+24, and VY and WU are diameters. Find m \widehat WUY.","In [Circle(Z)], [Equals(Angle(W,Z,X),Angle(X,Z,Y))], [Equals(MeasureOf(Angle(V,Z,U)),4x)] [Equals(MeasureOf(Angle(U,Z,Y)),2x+24)] and [IsDiameterOf(Line(V,Y),Circle($))], [IsDiameterOf(Line(W,U),Circle($))]. [Find(MeasureOf(Arc(W,U,Y)))]."
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
Use a Pythagorean Triple to find x.,[UseTheorem(Pythagorean_Triple)] to [Find(x)].
Find the value of the variable x in the figure.,[Find(x)].
What is the area of the parallelogram below? Round to the nearest whole number if necessary.,[Find(AreaOf(Parallelogram($)))]? Round to nearest whole number if necessary.
Use parallelogram JKLM to find m \angle MJK if JK = 2b+3 and JM = 3a.,"Use [Parallelogram(J,K,L,M)] to [Find(MeasureOf(Angle(M,J,K)))] if [Equals(LengthOf(Line(J,K)),2b+3)] and [Equals(LengthOf(Line(J,M)),3a)]."
Find LM.,"[Find(LengthOf(Line(L,M)))]."
Find the area of the rhombus.,[Find(AreaOf(Rhombus($)))].
"For isosceles trapezoid XYZW, find m \angle W.","For [Isosceles(Trapezoid(X,Y,Z,W))], [Find(MeasureOf(Angle(W)))]."
Find m \widehat JM.,"[Find(MeasureOf(Arc(J,M)))]."
Find y.,[Find(y)].
Find x.,[Find(x)].
"Quadrilateral ABCD is a rhombus. If DB = 2x-4 and PB = 2x-9, find PD."," [Rhombus(A,B,C,D)]. If [Equals(LengthOf(Line(D,B)),2x-4)] and [Equals(LengthOf(Line(P,B)),2x-9)] [Find(LengthOf(Line(P,D)))]."
"Find EG if \triangle ACB \sim \triangle EGF, AD is an altitude of \triangle ACB, EH is an altitude of \triangle EGF, AC = 17, AD = 15, and EH = 7.5.","[Find(LengthOf(Line(E,G)))] if [Similar(Triangle(A,C,B),Triangle(E,G,F))], [Equals(Line(A,D),AltitudeOf(Triangle(A,C,B)))], [Equals(Line(E,H),AltitudeOf(Triangle(E,G,F)))], [Equals(LengthOf(Line(A,C)),17)] [Equals(LengthOf(Line(A,D)),15)] and [Equals(LengthOf(Line(E,H)),7.5)]."
Find the measure of \angle T to the nearest tenth.,[Find(MeasureOf(Angle(T)))] to nearest tenth.
Find x so that m \parallel n.,"[Find(x)] so [Parallel(Line(m),Line(n))]."
Find m \angle 3.,[Find(MeasureOf(Angle(3)))].
"isosceles trapezoid TWYZ with \angle Z \cong \angle Y, m \angle Z = 30x, \angle T \cong \angle W, and m \angle T = 20x, find \angle Y.","[Isosceles(Trapezoid(T,W,Y,Z))] with [Equals(Angle(Z),Angle(Y))], [Equals(MeasureOf(Angle(Z)),30x)] [Equals(Angle(T),Angle(W))] and [Equals(MeasureOf(Angle(T)),20x)] [Find(MeasureOf(Angle(Y)))]."
Find the value of x.,[Find(x)].
"In circle F, what is the measure of \widehat EA if m \angle DFE is 36?","In [Circle(F)], [Find(MeasureOf(Arc(E,A)))] if [Equals(MeasureOf(Angle(D,F,E)),36)]?"
"\triangle DFG and \triangle FGH are isosceles, m \angle FDH = 28 and DG \cong FG \cong FH. Find the measure of \angle DGF.","[Isosceles(Triangle(D,F,G))], [Isosceles(Triangle(F,G,H))], [Equals(MeasureOf(Angle(F,D,H)),28)] and [Equals(LengthOf(Line(D,G)),Line(F,G))], [Equals(LengthOf(Line(F,G)),Line(F,H))]. [Find(MeasureOf(Angle(D,G,F)))]."
"In the figure, m \angle 4 = 101. Find the measure of \angle 7.",", [Equals(MeasureOf(Angle(4)),101)] [Find(MeasureOf(Angle(7)))]."
Point S is the incenter of \triangle JPL. Find SQ.,"[IsIncenterOf(Point(S),Triangle(J,P,L))]. [Find(LengthOf(Line(S,Q)))]."
"In \odot S, m \angle TSR = 42. Find m \widehat KRT.","In [Circle(S)], [Equals(MeasureOf(Angle(T,S,R)),42)] [Find(MeasureOf(Arc(K,R,T)))]."
Find the value of the variable m.,[Find(m)].
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
"In the figure, m \angle 9 = 75. Find the measure of \angle 11.",", [Equals(MeasureOf(Angle(9)),75)] [Find(MeasureOf(Angle(11)))]."
Find y.,[Find(y)].
Find m \angle 3.,[Find(MeasureOf(Angle(3)))].
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
Find x. Round side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
Point S is the incenter of \triangle JPL. Find QJ.,"[IsIncenterOf(Point(S),Triangle(J,P,L))]. [Find(LengthOf(Line(Q,J)))]."
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Find the measure of \angle 1.,[Find(MeasureOf(Angle(1)))].
"In the figure, m \angle 11 = 62 and m \angle 14 = 38. Find the measure of \angle 5.",", [Equals(MeasureOf(Angle(11)),62)] and [Equals(MeasureOf(Angle(14)),38)] [Find(MeasureOf(Angle(5)))]."
Find b.,[Find(b)].
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
"In \odot H, PQ = 3x-4 and RS = 14. Find x.","In [Circle(H)], [Equals(LengthOf(Line(P,Q)),3x-4)] and [Equals(LengthOf(Line(R,S)),14)] [Find(x)]."
"In \odot C, m \angle HCG = 2x and m \angle HCD = 6x+28, find m \widehat HGF.","In [Circle(C)], [Equals(MeasureOf(Angle(H,C,G)),2x)] and [Equals(MeasureOf(Angle(H,C,D)),6x+28)] [Find(MeasureOf(Arc(H,G,F)))]."
Refer to the figure at the right. Find the value of m \angle CBD if p \parallel q.,"[Shape($)]. [Find(MeasureOf(Angle(C,B,D)))] if [Parallel(Line(p),Line(q))]."
Find m \angle B.,[Find(MeasureOf(Angle(B)))].
Find QS if \triangle QRS is an equilateral triangle.,"[Find(LengthOf(Line(Q,S)))] if [Equilateral(Triangle(Q,R,S))] [Triangle($)]."
"In the figure, m \angle 1 = 53. Find the measure of \angle 7.",", [Equals(MeasureOf(Angle(1)),53)] [Find(MeasureOf(Angle(7)))]."
Find the value of x.,[Find(x)].
Find y.,[Find(y)].
"If WX = 7, WY = a, WV = 6, and VZ = a-9, find WY.","If [Equals(LengthOf(Line(W,X)),7)] [Equals(LengthOf(Line(W,Y)),a)] [Equals(LengthOf(Line(W,V)),6)] and [Equals(LengthOf(Line(V,Z)),a-9)] [Find(LengthOf(Line(W,Y)))]."
Find DE.,"[Find(LengthOf(Line(D,E)))]."
Find y.,[Find(y)].
"In the figure, m \angle 8 = 96 and m \angle 12 = 42. Find the measure of \angle 11.",", [Equals(MeasureOf(Angle(8)),96)] and [Equals(MeasureOf(Angle(12)),42)] [Find(MeasureOf(Angle(11)))]."
"\triangle EFG is equilateral, and EH bisects \angle E. Find m \angle 1.","[Equilateral(Triangle(E,F,G))] and [BisectsAngle(Line(E,H),Angle(E))]. [Find(MeasureOf(Angle(1)))]."
"a = 8, b = 15, and c = 17, find \cos A.","[Equals(a,8)] [Equals(b,15)] and [Equals(c,17)] [Find(CosOf(Angle(A)))]."
Find the variable of a to the nearest tenth. Assume that segments that appear to be tangent are tangent.,"[Find(a)] to nearest tenth. [Tangent(Line($),Circle($))]."
P is the incenter of \triangle AEC. Find PB. Rounded to the nearest hundredth.,"[IsIncenterOf(Point(P),Triangle(A,E,C))]. [Find(LengthOf(Line(P,B)))]. Rounded to nearest hundredth."
"Find DE if AB = 6, AF = 8, BC = x, CD = y, DE = 2y-3, and FE = x+\frac{10}{3}.","[Find(LengthOf(Line(D,E)))] if [Equals(LengthOf(Line(A,B)),6)] [Equals(LengthOf(Line(A,F)),8)] [Equals(LengthOf(Line(B,C)),x)] [Equals(LengthOf(Line(C,D)),y)] [Equals(LengthOf(Line(D,E)),2y-3)] and [Equals(LengthOf(Line(F,E)),x+\frac{10}{3})]."
Find the measure of \angle AFD on \odot F with diameter AC.,"[Find(MeasureOf(Angle(A,F,D)))] on [Circle(F)], [IsDiameterOf(Line(A,C),Circle(F))]."
"Find the perimeter of the figure. Round to the nearest hundredth, if necessary.","[Find(PerimeterOf(Shape($)))]. Round to nearest hundredth, if necessary."
The radius of \odot P is 5 and PR = 3. Find QR.,"[Equals(RadiusOf(Circle(P)),5)] and [Equals(LengthOf(Line(P,R)),3)] [Find(LengthOf(Line(Q,R)))]."
Find m \angle 3.,[Find(MeasureOf(Angle(3)))].
Find the area of the regular polygon. Round to the nearest tenth.,[Find(AreaOf(Regular(Polygon($))))]. Round to nearest tenth.
"In the figure, m \angle 1 = 94. Find the measure of \angle 4.",", [Equals(MeasureOf(Angle(1)),94)] [Find(MeasureOf(Angle(4)))]."
Find AP.,"[Find(LengthOf(Line(A,P)))]."
Find x.,[Find(x)].
"In the figure, m \angle 1 = 58, m \angle 2 = 47, and m \angle 3 = 26. Find the measure of \angle 6.",", [Equals(MeasureOf(Angle(1)),58)] [Equals(MeasureOf(Angle(2)),47)] and [Equals(MeasureOf(Angle(3)),26)] [Find(MeasureOf(Angle(6)))]."
Find m \angle D.,[Find(MeasureOf(Angle(D)))].
"ABCD is a rectangle. If CF = 4x+1 and DF = x+13, find x."," [Rectangle(A,B,C,D)]. If [Equals(LengthOf(Line(C,F)),4x+1)] and [Equals(LengthOf(Line(D,F)),x+13)] [Find(x)]."
Find x.,[Find(x)].
"If \overrightarrow AC bisects \angle DAB, BC = 4x+8, and DC = 9x-7, find BC.","If [BisectsAngle(Line(A,C),Angle(D,A,B))], [Equals(LengthOf(Line(B,C)),4x+8)] and [Equals(LengthOf(Line(D,C)),9x-7)] [Find(LengthOf(Line(B,C)))]."
Find x. Round the side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
Find x.,[Find(x)].
"In quadrilateral PQRS, PQ = 721, QR = 547, RS = 593, PS = 756, and m \angle P = 58. Find m \angle PQS.","In [Quadrilateral(P,Q,R,S)], [Equals(LengthOf(Line(P,Q)),721)] [Equals(LengthOf(Line(Q,R)),547)] [Equals(LengthOf(Line(R,S)),593)] [Equals(LengthOf(Line(P,S)),756)] and [Equals(MeasureOf(Angle(P)),58)] [Find(MeasureOf(Angle(P,Q,S)))]."
Find x.,[Find(x)].
"Suppose \angle 4 and \angle 5 form a linear pair. If m \angle 1 = 2x, m \angle 2 = 3x-20, and m \angle 3 = x-4, what is m \angle 3?","[Equals(SumOf(MeasureOf(Angle(4)),MeasureOf(Angle(4))),180)]. If [Equals(MeasureOf(Angle(1)),2x)] [Equals(MeasureOf(Angle(2)),3x-20)] and [Equals(MeasureOf(Angle(3)),x-4)] [Find(MeasureOf(Angle(3)))]?"
"\triangle DFG and \triangle FGH are isosceles, m \angle FDH = 28 and DG \cong FG \cong FH. Find the measure of \angle FGH.","[Isosceles(Triangle(D,F,G))], [Isosceles(Triangle(F,G,H))], [Equals(MeasureOf(Angle(F,D,H)),28)] and [Equals(LengthOf(Line(D,G)),Line(F,G))], [Equals(LengthOf(Line(F,G)),Line(F,H))]. [Find(MeasureOf(Angle(F,G,H)))]."
Find AC.,"[Find(LengthOf(Line(A,C)))]."
"If \sin x = 0.6 and AB = 12, what is the area of \triangle ABC?","If [Equals(SinOf(x),0.6)] and [Equals(LengthOf(Line(A,B)),12)] [Find(AreaOf(Triangle(A,B,C)))]?"
Find y.,[Find(y)].
Find m \angle T.,[Find(MeasureOf(Angle(T)))].
"In \odot S, m \angle TSR = 42. Find m \widehat ERT.","In [Circle(S)], [Equals(MeasureOf(Angle(T,S,R)),42)] [Find(MeasureOf(Arc(E,R,T)))]."
Find x.,[Find(x)].
Find the measure of \angle B. Round to the nearest degree.,[Find(MeasureOf(Angle(B)))]. Round to nearest degree.
Find AB.,"[Find(LengthOf(Line(A,B)))]."
Find y.,[Find(y)].
"In \odot S, LM = 16 and PN = 4x. What is x?","In [Circle(S)], [Equals(LengthOf(Line(L,M)),16)] and [Equals(LengthOf(Line(P,N)),4x)] [Find(x)]?"
"Find the perimeter of \triangle ADF, if \triangle ADF \sim \triangle BCE, BC = 24, EB = 12, CE = 18, and DF = 21.","[Find(PerimeterOf(Triangle(A,D,F)))], if [Similar(Triangle(A,D,F),Triangle(B,C,E))], [Equals(LengthOf(Line(B,C)),24)] [Equals(LengthOf(Line(E,B)),12)] [Equals(LengthOf(Line(C,E)),18)] and [Equals(LengthOf(Line(D,F)),21)]."
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
Find x.,[Find(x)].
Find m \angle D.,[Find(MeasureOf(Angle(D)))].
Find x so that p \parallel q.,"[Find(x)] so [Parallel(Line(p),Line(q))]."
Find m \widehat BC.,"[Find(MeasureOf(Arc(B,C)))]."
Find TY.,"[Find(LengthOf(Line(T,Y)))]."
"In \odot Z, \angle WZX \cong \angle XZY, m \angle VZU = 4x, m \angle UZY = 2x+24, and VY and WU are diameters. Find m \widehat XY.","In [Circle(Z)], [Equals(Angle(W,Z,X),Angle(X,Z,Y))], [Equals(MeasureOf(Angle(V,Z,U)),4x)] [Equals(MeasureOf(Angle(U,Z,Y)),2x+24)] and [IsDiameterOf(Line(V,Y),Circle($))], [IsDiameterOf(Line(W,U),Circle($))]. [Find(MeasureOf(Arc(X,Y)))]."
"In \triangle PQR, ZQ = 3a-11, ZP = a+5, PY = 2c-1, YR = 4c-11, m \angle PRZ = 4b-17, m \angle ZRQ = 3b-4, m \angle QYR = 7b+6, and m \angle PXR = 2a+10. If QY is a perpendicular bisector of PR, find b.","In [Triangle(P,Q,R)], [Equals(LengthOf(Line(Z,Q)),3a-11)] [Equals(LengthOf(Line(Z,P)),a+5)] [Equals(LengthOf(Line(P,Y)),2c-1)] [Equals(LengthOf(Line(Y,R)),4c-11)] [Equals(MeasureOf(Angle(P,R,Z)),4b-17)] [Equals(MeasureOf(Angle(Z,R,Q)),3b-4)] [Equals(MeasureOf(Angle(Q,Y,R)),7b+6)] and [Equals(MeasureOf(Angle(P,X,R)),2a+10)] If [IsPerpendicularBisectorOf(Line(Q,Y),Line(P,R))], [Find(b)]."
Find x.,[Find(x)].
"In \triangle DEF, P is the midpoint of DE, and Q is the midpoint of side DF. If EF = 3x+4 and PQ = 20, what is the value of x?","In [Triangle(D,E,F)], [IsMidpointOf(Point(P),Line(D,E))] and [IsMidpointOf(Point(Q),Line(D,F))]. If [Equals(LengthOf(Line(E,F)),3x+4)] and [Equals(LengthOf(Line(P,Q)),20)] [Find(x)]?"
Find m \angle BAC.,"[Find(MeasureOf(Angle(B,A,C)))]."
What is the perimeter of the right triangle below? Round your answer to the nearest tenth if necessary.,[Find(PerimeterOf(Right(Triangle($))))]? Round to nearest tenth if necessary.
Find x.,[Find(x)].
Find the measure of \angle 5 if AB \perp BC.,"[Find(MeasureOf(Angle(5)))] if [Perpendicular(Line(A,B),Line(B,C))]."
"Find the perimeter of the \triangle WZX, if \triangle WZX \sim \triangle SRT, ST = 6, WX = 5, and the perimeter of \triangle SRT = 15.","[Find(PerimeterOf(Triangle(W,Z,X)))], if [Similar(Triangle(W,Z,X),Triangle(S,R,T))], [Equals(LengthOf(Line(S,T)),6)] [Equals(LengthOf(Line(W,X)),5)] and [Equals(PerimeterOf(Triangle(S,R,T)),15)]."
Express the ratio of \sin V as a decimal to the nearest hundredth.,[Find(RatioOf(SinOf(Angle(V))))] to nearest hundredth.
Find m \angle CGB.,"[Find(MeasureOf(Angle(C,G,B)))]."
Find x.,[Find(x)].
"Use rectangle LMNP, parallelogram LKMJ to solve the problem. If MK = 6x, KL = 3x+2y, and JN = 14-x, find x.","Use [Rectangle(L,M,N,P)], [Parallelogram(L,K,M,J)] to. If [Equals(LengthOf(Line(M,K)),6x)] [Equals(LengthOf(Line(K,L)),3x+2y)] and [Equals(LengthOf(Line(J,N)),14-x)] [Find(x)]."
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Which of the following angle pairs are alternate exterior angles?,Which of following [Angle($)] pairs are alternate exterior angles?
"In the figure, m \angle 12 = 64. Find the measure of \angle 9.",", [Equals(MeasureOf(Angle(12)),64)] [Find(MeasureOf(Angle(9)))]."
"If m \angle CFD = 12a+45, find a so that \overrightarrow FC \perp \overrightarrow FD.","If [Equals(MeasureOf(Angle(C,F,D)),12a+45)] [Find(a)] so [Perpendicular(Line(F,C),Line(F,D))]."
"If m \angle BNC = 20, find m \widehat BC.","If [Equals(MeasureOf(Angle(B,N,C)),20)] [Find(MeasureOf(Arc(B,C)))]."
Find x so that m \parallel n.,"[Find(x)] so [Parallel(Line(m),Line(n))]."
Find the value of x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Find b in the given parallelogram.,[Find(b)] in [Parallelogram($)].
The segment is tangent to the circle. Find x.,"[Tangent(Line($),Circle($))] to [Circle($)]. [Find(x)]."
"If PR \parallel WX, WX = 10, XY = 6, WY = 8, RY = 5, and PS = 3, find PY.","If [Parallel(Line(P,R),Line(W,X))], [Equals(LengthOf(Line(W,X)),10)] [Equals(LengthOf(Line(X,Y)),6)] [Equals(LengthOf(Line(W,Y)),8)] [Equals(LengthOf(Line(R,Y)),5)] and [Equals(LengthOf(Line(P,S)),3)] [Find(LengthOf(Line(P,Y)))]."
AD and CG are diameters of \odot B. Find m \widehat AC.,"[IsDiameterOf(Line(A,D),Circle(B))], [IsDiameterOf(Line(C,G),Circle(B))]. [Find(MeasureOf(Arc(A,C)))]."
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find the value of x.,[Find(x)].
Find x.,[Find(x)].
"If b = 3, find a.","If [Equals(b,3)] [Find(a)]."
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
Find RT.,"[Find(LengthOf(Line(R,T)))]."
"In \odot E, EG = EF. Find AB.","In [Circle(E)], [Equals(LengthOf(Line(E,G)),Line(E,F))]. [Find(LengthOf(Line(A,B)))]."
"If the circumference of the circle is 16\pi units, what is the total area of the shaded regions?","If [Equals(CircumferenceOf(Circle($)),16\pi)] [Find(AreaOf(Shaded(Shape($))))]?"
Find the base of the parallelogram given its area with 2000 square units.,"[Find(BaseOf(Parallelogram($)))], [Equals(AreaOf(Parallelogram($)),2000)]."
Find the value of x in the figure at the right.,[Find(x)].
Find the area of the regular polygon. Round to the nearest tenth.,[Find(AreaOf(Regular(Polygon($))))]. Round to nearest tenth.
Find the perimeter of parallelogram ABCD to the nearest tenth.,"[Find(PerimeterOf(Parallelogram(A,B,C,D)))] to nearest tenth."
"In rhombus ABCD, m \angle DAB = 2, m \angle ADC and CB = 6. Find m \angle DAB.","In [Rhombus(A,B,C,D)], [Equals(MeasureOf(Angle(D,A,B)),2)] [MeasureOf(Angle(A,D,C))] and [Equals(LengthOf(Line(C,B)),6)] [Find(MeasureOf(Angle(D,A,B)))]."
"Quadrilateral WXYZ is a rectangle. If PY = 3x-5 and WP = 2x+11, find ZP."," [Rectangle(W,X,Y,Z)]. If [Equals(LengthOf(Line(P,Y)),3x-5)] and [Equals(LengthOf(Line(W,P)),2x+11)] [Find(LengthOf(Line(Z,P)))]."
"If a = 4, find c.","If [Equals(a,4)] [Find(c)]."
Find the area of the kite.,[Find(AreaOf(Kite($)))].
WXYZ is a square. If WT = 3. Find m \angle WYX.," [Square(W,X,Y,Z)]. If [Equals(LengthOf(Line(W,T)),3)] [Find(MeasureOf(Angle(W,Y,X)))]."
"In the figure, m \angle 3 = 133. Find m \angle 5.",", [Equals(MeasureOf(Angle(3)),133)] [Find(MeasureOf(Angle(5)))]."
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find the area of the shaded region. Round to the nearest tenth if necessary.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth if necessary.
Find PN.,"[Find(LengthOf(Line(P,N)))]."
Find AF.,"[Find(LengthOf(Line(A,F)))]."
Find m \widehat ES.,"[Find(MeasureOf(Arc(E,S)))]."
Find z.,[Find(z)].
Use parallelogram PQRS to find m \angle S.,"Use [Parallelogram(P,Q,R,S)] to [Find(MeasureOf(Angle(S)))]."
"Circle W has a radius of 4 units, \odot Z has a radius of 7 units, and XY = 2. Find IX.","[Equals(RadiusOf(Circle(W)),4)] [Equals(RadiusOf(Circle(Z)),7)] and [Equals(LengthOf(Line(X,Y)),2)] [Find(LengthOf(Line(I,X)))]."
Find the value of the variable x in the figure.,[Find(x)].
"Circles G, J, and K all intersect at L. If GH = 10. Find FG.","[IntersectAt(Circle(G),Circle(J),Circle(K),Point(L))]. If [Equals(LengthOf(Line(G,H)),10)] [Find(LengthOf(Line(F,G)))]."
Find y.,[Find(y)].
Find y.,[Find(y)].
Find JL.,"[Find(LengthOf(Line(J,L)))]."
"If m \widehat AE = 75, find m \angle ADE.","If [Equals(MeasureOf(Arc(A,E)),75)] [Find(MeasureOf(Angle(A,D,E)))]."
Find y.,[Find(y)].
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
"For the pair of similar figures, use the given areas to find x.","[Similar(Shape($1),Shape($2))], to [Find(x)]."
Find the measure of \angle 2.,[Find(MeasureOf(Angle(2)))].
Find y.,[Find(y)].
Find the value of x.,[Find(x)].
Find the perimeter of the triangle. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Triangle($)))]. Round to nearest tenth if necessary.
\triangle LMN \cong \triangle QRS. Find y.,"[Congruent(Triangle(L,M,N),Triangle(Q,R,S))]. [Find(y)]."
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
Find y.,[Find(y)].
Find m \angle 7.,[Find(MeasureOf(Angle(7)))].
Find m \angle YXW.,"[Find(MeasureOf(Angle(Y,X,W)))]."
"If m \angle F = 7x+2 and m \angle H = 17x-8, find x.","If [Equals(MeasureOf(Angle(F)),7x+2)] and [Equals(MeasureOf(Angle(H)),17x-8)] [Find(x)]."
Find y.,[Find(y)].
Find the measure of \angle A.,[Find(MeasureOf(Angle(A)))].
Find the area of the figure.,[Find(AreaOf(Shape($)))].
Circle O has a radius of 13 inches. Radius OB is perpendicular to chord CD which is 24 inches long. Find OX.,"[Equals(RadiusOf(Circle(O)),13)] [Equals(Line(O,B),Radius)] [IsChordOf(Line(C,D),Circle($))]. [Perpendicular(Line(O,B),Line(C,D))]. [Equals(Line(C,D),24)] [Find(LengthOf(Line(O,X)))]."
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Find m \angle CAM.,"[Find(MeasureOf(Angle(C,A,M)))]."
"In the figure below, \angle ABC is intersected by parallel lines l and m. What is the measure of \angle ABC? Express your answer in degrees.",", [Angle(A,B,C)]. [Parallel(Line(l),Line(m))]. [IntersectAt(Line(l),Line(m),Point(B))]. [Find(MeasureOf(Angle(A,B,C)))]?"
Find the value of x in the diagram.,[Find(x)].
Find the value of x.,[Find(x)].
"If XN = 6, XM = 2, and XY = 10, find NZ.","If [Equals(LengthOf(Line(X,N)),6)] [Equals(LengthOf(Line(X,M)),2)] and [Equals(LengthOf(Line(X,Y)),10)] [Find(LengthOf(Line(N,Z)))]."
Find y.,[Find(y)].
"Find CD if AC = x-3, BE = 20, AB = 16, and CD = x+5.","[Find(LengthOf(Line(C,D)))] if [Equals(LengthOf(Line(A,C)),x-3)] [Equals(LengthOf(Line(B,E)),20)] [Equals(LengthOf(Line(A,B)),16)] and [Equals(LengthOf(Line(C,D)),x+5)]."
Find the area of the shaded region. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth.
"JKLM is a rectangle. MLPR is a rhombus. \angle JMK \cong \angle RMP, m \angle JMK = 55, and m \angle MRP = 70. Find m \angle KML."," [Rectangle(J,K,L,M)]. [Rhombus(M,L,P,R)]. [Equals(Angle(J,M,K),Angle(R,M,P))], [Equals(MeasureOf(Angle(J,M,K)),55)] and [Equals(MeasureOf(Angle(M,R,P)),70)] [Find(MeasureOf(Angle(K,M,L)))]."
"In rhombus ABCD, m \angle DAB = 2, m \angle ADC and CB = 6. Find m \angle ACD.","In [Rhombus(A,B,C,D)], [Equals(MeasureOf(Angle(D,A,B)),2)] [MeasureOf(Angle(A,D,C))] and [Equals(LengthOf(Line(C,B)),6)] [Find(MeasureOf(Angle(A,C,D)))]."
"Find AE if AB = 12, AC = 16, and ED = 5.","[Find(LengthOf(Line(A,E)))] if [Equals(LengthOf(Line(A,B)),12)] [Equals(LengthOf(Line(A,C)),16)] and [Equals(LengthOf(Line(E,D)),5)]."
Use parallelogram MNPR to find m \angle RNP.,"Use [Parallelogram(M,N,P,R)] to [Find(MeasureOf(Angle(R,N,P)))]."
Find y in the figure.,[Find(y)].
"In \odot P, the radius is 2 inches, find the length of \widehat RS. Round to the nearest hundredth."," [Circle(P)], [Equals(RadiusOf(Circle(P)),2)] [Find(LengthOf(Arc(R,S)))]. Round to nearest hundredth."
Use parallelogram ABCD to find m \angle ADC.,"Use [Parallelogram(A,B,C,D)] to [Find(MeasureOf(Angle(A,D,C)))]."
The rectangle is inscribed into the circle. Find the exact circumference of the circle.,"[InscribedIn(Rectangle($),Circle($))]. [Find(CircumferenceOf(Circle($)))]."
Find DE.,"[Find(LengthOf(Line(D,E)))]."
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find the length of \widehat AB. Round to the nearest hundredth.,"[Find(LengthOf(Arc(A,B)))]. Round to nearest hundredth."
Find AB if \triangle ABC is an isosceles triangle with AB \cong BC.,"[Find(LengthOf(Line(A,B)))] if [Isosceles(Triangle(A,B,C))] with [Equals(LengthOf(Line(A,B)),Line(B,C))]."
Find m \angle BGE.,"[Find(MeasureOf(Angle(B,G,E)))]."
Find x. Round the side measure to the nearest tenth.,[Find(x)]. Round side measure to nearest tenth.
"For the pair of similar figures, use the given areas to find x.","[Similar(Shape($1),Shape($2))], to [Find(x)]."
Find x.,[Find(x)].
"In the figure, a regular polygon is inscribed in a circle. Find the measure of a central angle.",", [InscribedIn(Regular(Polygon($)),Circle($))]. [Find(MeasureOf(Angle($)))]."
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find XZ.,"[Find(LengthOf(Line(X,Z)))]."
"In regular hexagon UVWXYZ, the side is 12 centimeters long. Find WY."," [Regular(Hexagon(U,V,W,X,Y,Z))], [Equals(SideOf(Regular(Hexagon(U,V,W,X,Y,Z))),12)] [Find(LengthOf(Line(W,Y)))]."
Find the area of the figure.,[Find(AreaOf(Shape($)))].
Find x.,[Find(x)].
Let GH be the median of RSBA. Find GH.,"Let [IsMedianOf(Line(G,H),Quadrilateral(R,S,B,A))]. [Find(LengthOf(Line(G,H)))]."
Find x.,[Find(x)].
Find m \angle 2 if m \widehat BC = 30 and m \widehat AD = 20.,"[Find(MeasureOf(Angle(2)))] if [Equals(MeasureOf(Arc(B,C)),30)] and [Equals(MeasureOf(Arc(A,D)),20)]."
Find m \angle VXW.,"[Find(MeasureOf(Angle(V,X,W)))]."
Find WR.,"[Find(LengthOf(Line(W,R)))]."
Find m \angle RST.,"[Find(MeasureOf(Angle(R,S,T)))]."
"Polygon ABCD \sim polygon AEFG, m \angle AGF = 108, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26. Find m \angle ADC.","[Similar(Quadrilateral(A,B,C,D),Quadrilateral(A,E,F,G))], [Equals(MeasureOf(Angle(A,G,F)),108)] [Equals(LengthOf(Line(G,F)),14)] [Equals(LengthOf(Line(A,D)),12)] [Equals(LengthOf(Line(D,G)),4.5)] [Equals(LengthOf(Line(E,F)),8)] and [Equals(LengthOf(Line(A,B)),26)] [Find(MeasureOf(Angle(A,D,C)))]."
"In the figure, m \angle 3 = 110 and m \angle 12 = 55. Find the measure of \angle 1.",", [Equals(MeasureOf(Angle(3)),110)] and [Equals(MeasureOf(Angle(12)),55)] [Find(MeasureOf(Angle(1)))]."
Find x.,[Find(x)].
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Find x.,[Find(x)].
"MC = 7, RM = 4, and AT = 16. Find MB.","[Equals(LengthOf(Line(M,C)),7)] [Equals(LengthOf(Line(R,M)),4)] and [Equals(LengthOf(Line(A,T)),16)] [Find(LengthOf(Line(M,B)))]."
Find the value of the variable y in the figure.,[Find(y)].
Find y.,[Find(y)].
Find m \angle W.,[Find(MeasureOf(Angle(W)))].
"A plane travels from Des Moines to Phoenix, on to Atlanta, and back to Des Moines, as shown below. Find the distance in miles from Phoenix to Atlanta if the total trip was 3482 miles.","A plane travels from Des Moines to Phoenix, on to Atlanta and back to Des Moines,. Find distance in from Phoenix to Atlanta if trip was 3482."
Find m \angle R.,[Find(MeasureOf(Angle(R)))].
"In the figure, m \angle 1 = 58, m \angle 2 = 47, and m \angle 3 = 26. Find the measure of \angle 5.",", [Equals(MeasureOf(Angle(1)),58)] [Equals(MeasureOf(Angle(2)),47)] and [Equals(MeasureOf(Angle(3)),26)] [Find(MeasureOf(Angle(5)))]."
"The diagonals of rhombus FGHJ intersect at K. If GH = x+9 and JH = 5x-2, find x.","[Rhombus(F,G,H,J)]. [IsDiagonalOf(Line(F,H),Rhombus(F,G,H,J))], [IsDiagonalOf(Line(G,J),Rhombus(F,G,H,J))]. [IntersectAt(Line(F,H),Line(G,J),Point(K))]. If [Equals(LengthOf(Line(G,H)),x+9)] and [Equals(LengthOf(Line(J,H)),5x-2)] [Find(x)]."
Find x.,[Find(x)].
Find the circumference of the figure. Round to the nearest tenth.,[Find(CircumferenceOf(Shape($)))]. Round to nearest tenth.
"If m \widehat FE = 118, m \widehat AB = 108, m \angle EGB = 52, and m \angle EFB = 30, find m \widehat CF.","If [Equals(MeasureOf(Arc(F,E)),118)] [Equals(MeasureOf(Arc(A,B)),108)] [Equals(MeasureOf(Angle(E,G,B)),52)] and [Equals(MeasureOf(Angle(E,F,B)),30)] [Find(MeasureOf(Arc(C,F)))]."
Use a Pythagorean Triple to find x.,[UseTheorem(Pythagorean_Triple)] to [Find(x)].
Find the measure of \angle CFD on \odot F with diameter AC.,"[Find(MeasureOf(Angle(C,F,D)))] on [Circle(F)], [IsDiameterOf(Line(A,C),Circle(F))]."
"JKLM is a rectangle. MLPR is a rhombus. \angle JMK \cong \angle RMP, m \angle JMK = 55, and m \angle MRP = 70. Find m \angle KLP."," [Rectangle(J,K,L,M)]. [Rhombus(M,L,P,R)]. [Equals(Angle(J,M,K),Angle(R,M,P))], [Equals(MeasureOf(Angle(J,M,K)),55)] and [Equals(MeasureOf(Angle(M,R,P)),70)] [Find(MeasureOf(Angle(K,L,P)))]."
Find x. Round the angle measure to the nearest degree.,[Find(x)]. Round angle measure to nearest degree.
Q is the centroid and BE = 9. Find BQ.,"[IsCentroidOf(Point(Q),Shape($))] and [Equals(LengthOf(Line(B,E)),9)] [Find(LengthOf(Line(B,Q)))]."
"AB is a diameter, AC = 8 inches, and BC = 15 inches. Find the radius of the circle.","[IsDiameterOf(Line(A,B),Circle($))], [Equals(LengthOf(Line(A,C)),8)] and [Equals(LengthOf(Line(B,C)),15)] [Find(RadiusOf(Circle($)))]."
Find y.,[Find(y)].
"m is the perpendicular bisector of XZ, WZ = 14.9. Find WX.","[IsPerpendicularBisectorOf(Line(m),Line(X,Z))], [Equals(LengthOf(Line(W,Z)),14.9)] [Find(LengthOf(Line(W,X)))]."
"Lines l, m, and n are perpendicular bisectors of \triangle PQR and meet at T. If TQ = 2x, PT = 3y-1, and TR = 8, find z.","[IsPerpendicularBisectorOf(Line(l),Triangle(P,Q,R))], [IsPerpendicularBisectorOf(Line(m),Triangle(P,Q,R))], [IsPerpendicularBisectorOf(Line(n),Triangle(P,Q,R))]. [IntersectAt(Line(l),Line(m),Line(n),Point(T))]. If [Equals(LengthOf(Line(T,Q)),2x)] [Equals(LengthOf(Line(P,T)),3y-1)] and [Equals(LengthOf(Line(T,R)),8)] [Find(z)]."
"If AB = 12, AC = 16, and ED = 5, find AE.","If [Equals(LengthOf(Line(A,B)),12)] [Equals(LengthOf(Line(A,C)),16)] and [Equals(LengthOf(Line(E,D)),5)] [Find(LengthOf(Line(A,E)))]."
Find m \angle NCL.,"[Find(MeasureOf(Angle(N,C,L)))]."
Find the measure of the altitude drawn to the hypotenuse.,"[Find(LengthOf(AltitudeOf(Triangle($1,$2,$3))))], [IsHypotenuseOf(Line($1,$3),Triangle($1,$2,$3))]."
Find x.,[Find(x)].
"In rhombus LMPQ, m \angle QLM = 2x^{2}-10, m \angle QPM = 8x, and MP = 10. Find the perimeter of LMPQ.","In [Rhombus(L,M,P,Q)], [Equals(MeasureOf(Angle(Q,L,M)),2x^{2}-10)] [Equals(MeasureOf(Angle(Q,P,M)),8x)] and [Equals(LengthOf(Line(M,P)),10)] [Find(PerimeterOf(Quadrilateral(L,M,P,Q)))]."
Find the area of the trapezoid.,[Find(AreaOf(Trapezoid($)))].
"Triangle LMN is equilateral, and MP bisects LN. Find the measure of the side of \triangle LMN.","[Equilateral(Triangle(L,M,N))] and [BisectsAngle(Line(M,P),Line(L,N))]. [Find(LengthOf(SideOf(Triangle(L,M,N))))]."
Find x.,[Find(x)].
"parallelogram MNPQ with m \angle M = 10x and m \angle N = 20x, find \angle M.","[Parallelogram(M,N,P,Q)] with [Equals(MeasureOf(Angle(M)),10x)] and [Equals(MeasureOf(Angle(N)),20x)] [Find(MeasureOf(Angle(M)))]."
"If m \angle 5 = 7x-5 and m \angle 4 = 2x+23, find x.","If [Equals(MeasureOf(Angle(5)),7x-5)] and [Equals(MeasureOf(Angle(4)),2x+23)] [Find(x)]."
Use parallelogram MNPR to find m \angle RMN.,"Use [Parallelogram(M,N,P,R)] to [Find(MeasureOf(Angle(R,M,N)))]."
Find m \angle B.,[Find(MeasureOf(Angle(B)))].
"If \triangle LMN \sim \triangle QRS, QR = 35, RS = 37, SQ = 12, and NL = 5, find the perimeter of \triangle LMN.","If [Similar(Triangle(L,M,N),Triangle(Q,R,S))], [Equals(LengthOf(Line(Q,R)),35)] [Equals(LengthOf(Line(R,S)),37)] [Equals(LengthOf(Line(S,Q)),12)] and [Equals(LengthOf(Line(N,L)),5)] [Find(PerimeterOf(Triangle(L,M,N)))]."
The two polygons are similar. Find UT.,"two [Similar(Polygon($1),Polygon($2))]. [Find(LengthOf(Line(U,T)))]."
Find m \angle 6.,[Find(MeasureOf(Angle(6)))].
\odot P \cong \odot Q. Find x.,"[Congruent(Circle(P),Circle(Q))]. [Find(x)]."
Find x.,[Find(x)].
Find QP.,"[Find(LengthOf(Line(Q,P)))]."
Find x.,[Find(x)].
"In rhombus ABCD, AB = 2x+3 and BC = 5x. Find m \angle AEB.","In [Rhombus(A,B,C,D)], [Equals(LengthOf(Line(A,B)),2x+3)] and [Equals(LengthOf(Line(B,C)),5x)] [Find(MeasureOf(Angle(A,E,B)))]."
"Circle O has a radius of 13 inches. Radius OB is perpendicular to chord CD which is 24 inches long. If m \widehat CD = 134, find m \widehat CB.","[Equals(RadiusOf(Circle(O)),13)] [Equals(Line(O,B),Radius)] [IsChordOf(Line(C,D),Circle($))]. [Perpendicular(Line(O,B),Line(C,D))]. [Equals(Line(C,D),24)] If [Equals(MeasureOf(Arc(C,D)),134)] [Find(MeasureOf(Arc(C,B)))]."
"Circles G, J, and K all intersect at L. If GH = 10, find FH.","[IntersectAt(Circle(G),Circle(J),Circle(K),Point(L))]. If [Equals(LengthOf(Line(G,H)),10)] [Find(LengthOf(Line(F,H)))]."
Find the scale factor from W to W'.,"[Find(ScaleFactorOf(Shape(W),Shape(W')))]."
Find m \angle R.,[Find(MeasureOf(Angle(R)))].
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Express the ratio of \cos B as a decimal to the nearest hundredth.,[Find(RatioOf(CosOf(Angle(B))))] to nearest hundredth.
AB \cong DF. Find x.,"[Equals(LengthOf(Line(A,B)),Line(D,F))]. [Find(x)]."
"In \odot M, FL = 24, HJ = 48, and m \widehat HP = 65. Find FG.","In [Circle(M)], [Equals(LengthOf(Line(F,L)),24)] [Equals(LengthOf(Line(H,J)),48)] and [Equals(MeasureOf(Arc(H,P)),65)] [Find(LengthOf(Line(F,G)))]."
Find x.,[Find(x)].
Find z.,[Find(z)].
Find x.,[Find(x)].
"In H, the diameter is 18, LM = 12, and m \widehat LM = 84. Find HP. Round to the nearest hundredth."," [Circle(H)], [Equals(DiameterOf(Circle(H)),18)] [Equals(LengthOf(Line(L,M)),12)] and [Equals(MeasureOf(Arc(L,M)),84)] [Find(LengthOf(Line(H,P)))]. Round to nearest hundredth."
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
Find x.,[Find(x)].
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
"In \triangle PQR, ST \parallel RQ. If PS = 12.5, SR = 5, and PT = 15, find TQ.","In [Triangle(P,Q,R)], [Parallel(Line(S,T),Line(R,Q))]. If [Equals(LengthOf(Line(P,S)),12.5)] [Equals(LengthOf(Line(S,R)),5)] and [Equals(LengthOf(Line(P,T)),15)] [Find(LengthOf(Line(T,Q)))]."
Find m \angle 4.,[Find(MeasureOf(Angle(4)))].
Find the area of the shaded region. ,[Find(AreaOf(Shaded(Shape($))))].
Find x to the nearest hundredth.,[Find(x)] to nearest hundredth.
Find the area of the rhombus.,[Find(AreaOf(Rhombus($)))].
Use parallelogram JKLM to find m \angle KJL if JK = 2b+3 and JM = 3a.,"Use [Parallelogram(J,K,L,M)] to [Find(MeasureOf(Angle(K,J,L)))] if [Equals(LengthOf(Line(J,K)),2b+3)] and [Equals(LengthOf(Line(J,M)),3a)]."
Find x if \triangle JLM \sim \triangle QST.,"[Find(x)] if [Similar(Triangle(J,L,M),Triangle(Q,S,T))]."
Find x.,[Find(x)].
"In the figure, m \angle 1 = 123. Find the measure of \angle 14.",", [Equals(MeasureOf(Angle(1)),123)] [Find(MeasureOf(Angle(14)))]."
"Circle J has a radius of 10 units, \odot K has a radius of 8 units, and BC = 5.4 units. Find JK.","[Equals(RadiusOf(Circle(J)),10)] [Equals(RadiusOf(Circle(K)),8)] and [Equals(LengthOf(Line(B,C)),5.4)] [Find(LengthOf(Line(J,K)))]."
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Find x.,[Find(x)].
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
"Find KJ if GJ = 8, GH = 12, and HI = 4.","[Find(LengthOf(Line(K,J)))] if [Equals(LengthOf(Line(G,J)),8)] [Equals(LengthOf(Line(G,H)),12)] and [Equals(LengthOf(Line(H,I)),4)]."
\triangle RST \cong \triangle ABC. Find x.,"[Congruent(Triangle(R,S,T),Triangle(A,B,C))]. [Find(x)]."
\triangle RSV \cong \triangle TVS. Find x.,"[Congruent(Triangle(R,S,V),Triangle(T,V,S))]. [Find(x)]."
"\overrightarrow BA and \overrightarrow BC are opposite rays and \overrightarrow BD bisects \angle ABF. If m \angle FBC = 2x+25 and m \angle ABF = 10x-1, find m \angle DBF.","[Line(B,A)], [Line(B,C)], [PointLiesOnLine(B,Line(A,C))] and [BisectsAngle(Line(B,D),Angle(A,B,F))]. If [Equals(MeasureOf(Angle(F,B,C)),2x+25)] and [Equals(MeasureOf(Angle(A,B,F)),10x-1)] [Find(MeasureOf(Angle(D,B,F)))]."
Express the ratio of \cos X as a decimal to the nearest hundredth.,[Find(RatioOf(CosOf(Angle(X))))] to nearest hundredth.
Find m \angle RCM.,"[Find(MeasureOf(Angle(R,C,M)))]."
"AB \perp DC and GH \perp FE. If \triangle ACD \sim \triangle GEF, find AB.","[Perpendicular(Line(A,B),Line(D,C))] and [Perpendicular(Line(G,H),Line(F,E))]. If [Similar(Triangle(A,C,D),Triangle(G,E,F))], [Find(LengthOf(Line(A,B)))]."
"Find x for the equilateral triangle RST if RS = x+9, ST = 2x, and RT = 3x-9.","[Find(x)] for [Equilateral(Triangle(R,S,T))] if [Equals(LengthOf(Line(R,S)),x+9)] [Equals(LengthOf(Line(S,T)),2x)] and [Equals(LengthOf(Line(R,T)),3x-9)]."
"Find x if AE = 3, AB = 2, BC = 6, and ED = 2x-3.","[Find(x)] if [Equals(LengthOf(Line(A,E)),3)] [Equals(LengthOf(Line(A,B)),2)] [Equals(LengthOf(Line(B,C)),6)] and [Equals(LengthOf(Line(E,D)),2x-3)]."
The pair of polygons is similar. Find x.,"[Similar(Polygon($1),Polygon($2))]. [Find(x)]."
"In \odot Z, \angle WZX \cong \angle XZY, m \angle VZU = 4x, m \angle UZY = 2x+24, and VY and WU are diameters. Find m \widehat WUX.","In [Circle(Z)], [Equals(Angle(W,Z,X),Angle(X,Z,Y))], [Equals(MeasureOf(Angle(V,Z,U)),4x)] [Equals(MeasureOf(Angle(U,Z,Y)),2x+24)] and [IsDiameterOf(Line(V,Y),Circle($))], [IsDiameterOf(Line(W,U),Circle($))]. [Find(MeasureOf(Arc(W,U,X)))]."
"Given that the perimeter of \triangle ABC = 25, find x. Assume that segments that appear tangent to circles are tangent.","[Equals(PerimeterOf(Triangle(A,B,C)),25)] [Find(x)]. Assume [Tangent(Line($),Circle($))]."
Find the measure of \angle 2 if AB \perp BC.,"[Find(MeasureOf(Angle(2)))] if [Perpendicular(Line(A,B),Line(B,C))]."
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find the area of the figure. Round to the nearest tenth.,[Find(AreaOf(Shape($)))]. Round to nearest tenth.
Find x.,[Find(x)].
Find m \angle K.,[Find(MeasureOf(Angle(K)))].
Find the perimeter of the triangle. Round to the nearest hundredth.,[Find(PerimeterOf(Triangle($)))]. Round to nearest hundredth.
Find x.,[Find(x)].
Find JQ if Q is the incenter of \triangle JLN. Rounded to the nearest hundredth.,"[Find(LengthOf(Line(J,Q)))] if [IsIncenterOf(Point(Q),Triangle(J,L,N))]. Rounded to nearest hundredth."
EB \parallel DC. Find x.,"[Parallel(Line(E,B),Line(D,C))]. [Find(x)]."
Refer to the triangle shown below. Find y to the nearest tenth.,[Triangle($)]. [Find(y)] to nearest tenth.
"The diameters of \odot A, \odot B, and \odot C are 10, 30 and 10 units, respectively. Find ZX if AZ \cong CW and CW = 2.","[Equals(DiameterOf(Circle(A)),10)] [Equals(DiameterOf(Circle(B)),30)] [Equals(DiameterOf(Circle(C)),10)] [Find(LengthOf(Line(Z,X)))] if [Equals(LengthOf(Line(A,Z)),Line(C,W))] and [Equals(LengthOf(Line(C,W)),2)]."
Find the measure of \angle AFB on \odot F with diameter AC.,"[Find(MeasureOf(Angle(A,F,B)))] on [Circle(F)], [IsDiameterOf(Line(A,C),Circle(F))]."
Find the measure of \angle 3 in the figure.,[Find(MeasureOf(Angle(3)))].
"In \odot M, FL = 24, HJ = 48, and m \widehat HP = 65. Find m \widehat PJ.","In [Circle(M)], [Equals(LengthOf(Line(F,L)),24)] [Equals(LengthOf(Line(H,J)),48)] and [Equals(MeasureOf(Arc(H,P)),65)] [Find(MeasureOf(Arc(P,J)))]."
Find the measure of \angle 3 if AB \perp BC.,"[Find(MeasureOf(Angle(3)))] if [Perpendicular(Line(A,B),Line(B,C))]."
Find m \angle A of quadrilateral ABCD.,"[Find(MeasureOf(Angle(A)))] of [Quadrilateral(A,B,C,D)]."
Find the scale factor from Q to Q'.,"[Find(ScaleFactorOf(Shape(Q),Shape(Q')))]."
"Find the perimeter of \triangle BCD, if \triangle BCD \sim \triangle FDE, CD = 12, FD = 5, FE = 4, and DE = 8.","[Find(PerimeterOf(Triangle(B,C,D)))], if [Similar(Triangle(B,C,D),Triangle(F,D,E))], [Equals(LengthOf(Line(C,D)),12)] [Equals(LengthOf(Line(F,D)),5)] [Equals(LengthOf(Line(F,E)),4)] and [Equals(LengthOf(Line(D,E)),8)]."
Use parallelogram JKLM to find m \angle KLM.,"Use [Parallelogram(J,K,L,M)] to [Find(MeasureOf(Angle(K,L,M)))]."
Find the area of the shaded region. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth.
Find the area of the shaded sector. Round to the nearest tenth.,[Find(AreaOf(Shaded(Sector($))))]. Round to nearest tenth.
Find x.,[Find(x)].
"Quadrilateral DEFG is a rectangle. If m \angle EDF = 5x-3 and m \angle DFG = 3x+7, find m \angle EDF."," [Rectangle(D,E,F,G)]. If [Equals(MeasureOf(Angle(E,D,F)),5x-3)] and [Equals(MeasureOf(Angle(D,F,G)),3x+7)] [Find(MeasureOf(Angle(E,D,F)))]."
"If AE = m-2, EC = m+4, AD = 4, and AB = 20, find m.","If [Equals(LengthOf(Line(A,E)),m-2)] [Equals(LengthOf(Line(E,C)),m+4)] [Equals(LengthOf(Line(A,D)),4)] and [Equals(LengthOf(Line(A,B)),20)] [Find(m)]."
"In rhombus ABCD, AB = 2x+3 and BC = 5x. Find AD.","In [Rhombus(A,B,C,D)], [Equals(LengthOf(Line(A,B)),2x+3)] and [Equals(LengthOf(Line(B,C)),5x)] [Find(LengthOf(Line(A,D)))]."
"If XM = 4, XN = 6, and NZ = 9, find XY.","If [Equals(LengthOf(Line(X,M)),4)] [Equals(LengthOf(Line(X,N)),6)] and [Equals(LengthOf(Line(N,Z)),9)] [Find(LengthOf(Line(X,Y)))]."
Which segments are parallel?,Which segments are parallel?
"In the figure, m \angle 11 = 62 and m \angle 14 = 38. Find the measure of \angle 1.",", [Equals(MeasureOf(Angle(11)),62)] and [Equals(MeasureOf(Angle(14)),38)] [Find(MeasureOf(Angle(1)))]."
Find y.,[Find(y)].
Use parallelogram JKLM to find m \angle JKL.,"Use [Parallelogram(J,K,L,M)] to [Find(MeasureOf(Angle(J,K,L)))]."
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find x.,[Find(x)].
Find RS if \triangle QRS is an equilateral triangle.,"[Find(LengthOf(Line(R,S)))] if [Equilateral(Triangle(Q,R,S))] [Triangle($)]."
Find x.,[Find(x)].
Find x. ,[Find(x)].
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find the area of the figure. Round to the nearest tenth.,[Find(AreaOf(Shape($)))]. Round to nearest tenth.
Use parallelogram JKLM to find m \angle KJL.,"Use [Parallelogram(J,K,L,M)] to [Find(MeasureOf(Angle(K,J,L)))]."
Find the area of the shaded region. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. Round to nearest tenth.
Find \tan X.,[Find(TanOf(Angle(X)))].
Find the height of the parallelogram given its area with 2000 square units.,"[Find(HeightOf(Parallelogram($)))], [Equals(AreaOf(Parallelogram($)),2000)]."
"Quadrilateral EFGH is a rectangle. If m \angle HGE = 13, find m \angle FGE."," [Rectangle(E,F,G,H)]. If [Equals(MeasureOf(Angle(H,G,E)),13)] [Find(MeasureOf(Angle(F,G,E)))]."
Find x in the parallelogram.,[Find(x)] in [Parallelogram($)].
Find \angle 5.,[Find(MeasureOf(Angle(5)))].
"In the figure, KL is tangent to \odot M at K. Find the value of x.",", [Tangent(Line(K,L),Circle(M))] at K. [Find(x)]."
Find x.,[Find(x)].
Find m \angle MPQ.,"[Find(MeasureOf(Angle(M,P,Q)))]."
Find m \angle 1 in the figure.,[Find(MeasureOf(Angle(1)))].
GJ is a diameter of \odot K. Find m \widehat GLJ.,"[IsDiameterOf(Line(G,J),Circle(K))]. [Find(MeasureOf(Arc(G,L,J)))]."
Find m \angle S.,[Find(MeasureOf(Angle(S)))].
Find XY of isosceles \triangle XYZ.,"[Find(LengthOf(Line(X,Y)))] of [Isosceles(Triangle(X,Y,Z))]."
Find x.,[Find(x)].
"Find x. Round to the nearest tenth, if necessary.","[Find(x)]. Round to nearest tenth, if necessary."
Find the area of the parallelogram.,[Find(AreaOf(Parallelogram($)))].
"AB is a diameter, AC = 8 inches, and BC = 15 inches. Find the circumference of the circle.","[IsDiameterOf(Line(A,B),Circle($))], [Equals(LengthOf(Line(A,C)),8)] and [Equals(LengthOf(Line(B,C)),15)] [Find(CircumferenceOf(Circle($)))]."
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Find PN.,"[Find(LengthOf(Line(P,N)))]."
"If LK = 4, MP = 3, PQ = 6, KJ = 2, RS = 6, and LP = 2, find ML.","If [Equals(LengthOf(Line(L,K)),4)] [Equals(LengthOf(Line(M,P)),3)] [Equals(LengthOf(Line(P,Q)),6)] [Equals(LengthOf(Line(K,J)),2)] [Equals(LengthOf(Line(R,S)),6)] and [Equals(LengthOf(Line(L,P)),2)] [Find(LengthOf(Line(M,L)))]."
"In the figure, m \angle 4 = 101. Find the measure of \angle 6.",", [Equals(MeasureOf(Angle(4)),101)] [Find(MeasureOf(Angle(6)))]."
Express the ratio of \sin P as a decimal to the nearest hundredth.,[Find(RatioOf(SinOf(Angle(P))))] to nearest hundredth.
Find x.,[Find(x)].
Find the measure of \angle 2.,[Find(MeasureOf(Angle(2)))].
m \angle 3 = x-12 and m \angle 6 = 72. Find x.,"[Equals(MeasureOf(Angle(3)),x-12)] and [Equals(MeasureOf(Angle(6)),72)] [Find(x)]."
Find x.,[Find(x)].
"Find GI if GH = 9, GK = 6, and KJ = 4.","[Find(LengthOf(Line(G,I)))] if [Equals(LengthOf(Line(G,H)),9)] [Equals(LengthOf(Line(G,K)),6)] and [Equals(LengthOf(Line(K,J)),4)]."
A regular pentagon and a square share a mutual vertex X. The sides XY and XZ are sides of a third regular polygon with a vertex at X. How many sides does this polygon have?,"[Regular(Pentagon($))] and[Square($)] share a mutual vertex X. [Equals(Line(X,Y),SideOf(Regular(Polygon($))))], [Equals(Line(X,Z),SideOf(Regular(Polygon($))))] of third [Regular(Polygon($))] with a vertex at X. How many sides does [Polygon($)] have?"
Find the area of the shaded region.,[Find(AreaOf(Shaded(Shape($))))].
Find the side length in isosceles triangle DEF.,"[Find(SideOf(Regular(Polygon($))))] in [Isosceles(Triangle(D,E,F))]."
Find the area of the triangle.,[Find(AreaOf(Triangle($)))].
"The diameter of \odot S is 30 units, the diameter of \odot R is 20 units, and DS = 9 units. Find RC.","[Equals(DiameterOf(Circle(S)),30)] [Equals(DiameterOf(Circle(R)),20)] and [Equals(LengthOf(Line(D,S)),9)] [Find(LengthOf(Line(R,C)))]."
Find x.,[Find(x)].
Equilateral pentagon PQRST is inscribed in \odot U. Find m \widehat QR.,"[InscribedIn(Equilateral(Pentagon(P,Q,R,S,T)),Circle(U))]. [Find(MeasureOf(Arc(Q,R)))]."
"Find the perimeter of \triangle RUW if \triangle RUW \sim \triangle STV, ST = 24, VS = 12, VT = 18 and UW = 21.","[Find(PerimeterOf(Triangle(R,U,W)))] if [Similar(Triangle(R,U,W),Triangle(S,T,V))], [Equals(LengthOf(Line(S,T)),24)] [Equals(LengthOf(Line(V,S)),12)] [Equals(LengthOf(Line(V,T)),18)] and [Equals(LengthOf(Line(U,W)),21)]."
"If ST = 8, TR = 4, and PT = 6, find QR.","If [Equals(LengthOf(Line(S,T)),8)] [Equals(LengthOf(Line(T,R)),4)] and [Equals(LengthOf(Line(P,T)),6)] [Find(LengthOf(Line(Q,R)))]."
Find x.,[Find(x)].
Find AD.,"[Find(LengthOf(Line(A,D)))]."
Find x.,[Find(x)].
"If LK = 4, MP = 3, PQ = 6, KJ = 2, RS = 6, and LP = 2, find JH.","If [Equals(LengthOf(Line(L,K)),4)] [Equals(LengthOf(Line(M,P)),3)] [Equals(LengthOf(Line(P,Q)),6)] [Equals(LengthOf(Line(K,J)),2)] [Equals(LengthOf(Line(R,S)),6)] and [Equals(LengthOf(Line(L,P)),2)] [Find(LengthOf(Line(J,H)))]."
Find x.,[Find(x)].
m \widehat AC = 160 and m \angle BEC = 38. What is m \angle AEB?,"[Equals(MeasureOf(Arc(A,C)),160)] and [Equals(MeasureOf(Angle(B,E,C)),38)] [Find(MeasureOf(Angle(A,E,B)))]?"
Find x.,[Find(x)].
Find BC.,"[Find(LengthOf(Line(B,C)))]."
"Triangle LMN is equilateral, and MP bisects LN. Find y.","[Equilateral(Triangle(L,M,N))] and [BisectsAngle(Line(M,P),Line(L,N))]. [Find(y)]."
"In \odot M, FL = 24, HJ = 48, and m \widehat HP = 65. Find m \widehat HJ.","In [Circle(M)], [Equals(LengthOf(Line(F,L)),24)] [Equals(LengthOf(Line(H,J)),48)] and [Equals(MeasureOf(Arc(H,P)),65)] [Find(MeasureOf(Arc(H,J)))]."
Find y.,[Find(y)].
"\overrightarrow QP and \overrightarrow QR are opposite rays, and \overrightarrow QT bisects \angle SQR. If m \angle SQR = 6x+8 and m \angle TQR = 4x-14, find m \angle SQT.","[Line(Q,P)], [Line(Q,R)], [PointLiesOnLine(Q,Line(P,R))] and [BisectsAngle(Line(Q,T),Angle(S,Q,R))]. If [Equals(MeasureOf(Angle(S,Q,R)),6x+8)] and [Equals(MeasureOf(Angle(T,Q,R)),4x-14)] [Find(MeasureOf(Angle(S,Q,T)))]."
Find y.,[Find(y)].
Find x. Assume that any segment that appears to be tangent is tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
"\triangle EFG is equilateral, and EH bisects \angle E. Find m \angle 2.","[Equilateral(Triangle(E,F,G))] and [BisectsAngle(Line(E,H),Angle(E))]. [Find(MeasureOf(Angle(2)))]."
Find y.,[Find(y)].
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
"In \triangle DEF, m \angle E = 108, m \angle F = 26, and f = 20. Find d to the nearest whole number.","In [Triangle(D,E,F)], [Equals(MeasureOf(Angle(E)),108)] [Equals(MeasureOf(Angle(F)),26)] and [Equals(f,20)] [Find(d)] to nearest whole number."
Find x.,[Find(x)].
"Quadrilateral EFGH is a rectangle. If FK = 32 feet, find EG."," [Rectangle(E,F,G,H)]. If [Equals(LengthOf(Line(F,K)),32)] [Find(LengthOf(Line(E,G)))]."
Find x.,[Find(x)].
Find ST.,"[Find(LengthOf(Line(S,T)))]."
"For the pair of similar figures, find the area of the green figure.","[Similar(Shape($1),Shape($2))], [Find(AreaOf(Green(Shape($))))]."
"For trapezoid ABCD, S and T are midpoints of the legs. If AB = x+4, CD = 3x+2, and ST = 9, find AB.","[Trapezoid(A,B,C,D)], [IsMidpointOf(Point(S),LegOf(Trapezoid(A,B,C,D)))], [IsMidpointOf(Point(T),LegOf(Trapezoid(A,B,C,D)))],. If [Equals(LengthOf(Line(A,B)),x+4)] [Equals(LengthOf(Line(C,D)),3x+2)] and [Equals(LengthOf(Line(S,T)),9)] [Find(LengthOf(Line(A,B)))]."
"m \angle 9 = 2x-4, m \angle 10 = 2x+4. Find the measure of \angle 10.","[Equals(MeasureOf(Angle(9)),2x-4)] [Equals(MeasureOf(Angle(10)),2x+4)] [Find(MeasureOf(Angle(10)))]."
"Quadrilateral DEFG is a rectangle. If m \angle EFD = 2x-3 and m \angle DFG = x+12, find m \angle EFD."," [Rectangle(D,E,F,G)]. If [Equals(MeasureOf(Angle(E,F,D)),2x-3)] and [Equals(MeasureOf(Angle(D,F,G)),x+12)] [Find(MeasureOf(Angle(E,F,D)))]."
What is the area of \parallelogram ABCD?,"[Find(AreaOf(Parallelogram(A,B,C,D)))]?"
Find x.,[Find(x)].
"In \odot M, FL = 24, HJ = 48, and m \widehat HP = 65. Find NJ.","In [Circle(M)], [Equals(LengthOf(Line(F,L)),24)] [Equals(LengthOf(Line(H,J)),48)] and [Equals(MeasureOf(Arc(H,P)),65)] [Find(LengthOf(Line(N,J)))]."
"In the figure, m \angle 9 = 75. Find the measure of \angle 6.",", [Equals(MeasureOf(Angle(9)),75)] [Find(MeasureOf(Angle(6)))]."
"Find BD if BF bisects \angle ABC and AC \parallel ED, BA = 6, BC = 7.5, AC = 9, and DE = 9.","[Find(LengthOf(Line(B,D)))] if [BisectsAngle(Line(B,F),Angle(A,B,C))] and [Parallel(Line(A,C),Line(E,D))], [Equals(LengthOf(Line(B,A)),6)] [Equals(LengthOf(Line(B,C)),7.5)] [Equals(LengthOf(Line(A,C)),9)] and [Equals(LengthOf(Line(D,E)),9)]."
Find x so that a \parallel b.,"[Find(x)] so [Parallel(Line(a),Line(b))]."
"In the figure, \triangle ABC \sim \triangle DEF. BG is a median of \triangle ABC, and EH is a median of \triangle DEF. Find EH if BC = 30, BG = 15, and EF = 15.",", [Similar(Triangle(A,B,C),Triangle(D,E,F))]. [IsMedianOf(Line(B,G),Triangle(A,B,C))] and [IsMedianOf(Line(E,H),Triangle(D,E,F))]. [Find(LengthOf(Line(E,H)))] if [Equals(LengthOf(Line(B,C)),30)] [Equals(LengthOf(Line(B,G)),15)] and [Equals(LengthOf(Line(E,F)),15)]."
"m \angle 2 = 2x, m \angle 3 = x. Find m \angle 3.","[Equals(MeasureOf(Angle(2)),2x)] [Equals(MeasureOf(Angle(3)),x)] [Find(MeasureOf(Angle(3)))]."
XY and XZ are midsegments of \triangle RST. Find ST.,"[IsMidsegmentOf(Line(X,Y),Triangle(R,S,T))], [IsMidsegmentOf(Line(X,Z),Triangle(R,S,T))]. [Find(LengthOf(Line(S,T)))]."
Find TX if EX = 24 and DE = 7.,"[Find(LengthOf(Line(T,X)))] if [Equals(LengthOf(Line(E,X)),24)] and [Equals(LengthOf(Line(D,E)),7)]."
Find the value of the variable x in the figure.,[Find(x)].
What is the value of x below to the nearest tenth?,[Find(x)] to nearest tenth?
\triangle KLN and \triangle LMN are isosceles and m \angle JKN = 130. Find the measure of \angle J.,"[Isosceles(Triangle(K,L,N))], [Isosceles(Triangle(L,M,N))] and [Equals(MeasureOf(Angle(J,K,N)),130)] [Find(MeasureOf(Angle(J)))]."
Find QM.,"[Find(LengthOf(Line(Q,M)))]."
Find x. Assume that any segment that appears to be tangent is tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find m \angle ABC.,"[Find(MeasureOf(Angle(A,B,C)))]."
Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. Round to nearest tenth if necessary. [Tangent(Line($),Circle($))]."
Find x in the figure.,[Find(x)].
Find BC.,"[Find(LengthOf(Line(B,C)))]."
Find h in the triangle.,[Find(h)] in [Triangle($)].
Find the measure of \angle A to the nearest tenth.,[Find(MeasureOf(Angle(A)))] to nearest tenth.
Find x so that m \parallel n.,"[Find(x)] so [Parallel(Line(m),Line(n))]."
Find the value of x.,[Find(x)].
Find x.,[Find(x)].
Find x.,[Find(x)].
"Quadrilateral ABCD is inscribed in \odot Z such that m \angle BZA = 104, m \widehat CB = 94, and AB \parallel DC. Find m \angle ZAC.","[InscribedIn(Quadrilateral(A,B,C,D),Circle(Z))] [Equals(MeasureOf(Angle(B,Z,A)),104)] [Equals(MeasureOf(Arc(C,B)),94)] and [Parallel(Line(A,B),Line(D,C))]. [Find(MeasureOf(Angle(Z,A,C)))]."
"a = 14, b = 48, and c = 50, find \sin A.","[Equals(a,14)] [Equals(b,48)] and [Equals(c,50)] [Find(SinOf(Angle(A)))]."
Quadrilateral WXYZ is a rectangle. Find the measure of \angle 6 if m \angle 1 = 30.," [Rectangle(W,X,Y,Z)]. [Find(MeasureOf(Angle(6)))] if [Equals(MeasureOf(Angle(1)),30)]."
Find the area of the regular polygon figure. Round to the nearest tenth.,[Find(AreaOf(Regular(Polygon($))))]. Round to nearest tenth.
Find y.,[Find(y)].
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find \widehat WN if \triangle IWN is equilateral and WN = 5.,"[Find(Arc(W,N))] if [Equilateral(Triangle(I,W,N))] and [Equals(LengthOf(Line(W,N)),5)]."
Find x.,[Find(x)].
Find the measure of the altitude drawn to the hypotenuse.,"[Find(LengthOf(AltitudeOf(Triangle($1,$2,$3))))], [IsHypotenuseOf(Line($1,$3),Triangle($1,$2,$3))]."
HK and IG are diameters of \odot L. Find m \widehat IHJ.,"[IsDiameterOf(Line(H,K),Circle(L))], [IsDiameterOf(Line(I,G),Circle(L))]. [Find(MeasureOf(Arc(I,H,J)))]."
"Trapezoid GHJK has an area of 188.35 square feet. If HJ is 16.5 feet, find GK.","[Equals(AreaOf(Trapezoid(G,H,J,K)),188.35)] If [Equals(Line(H,J),16.5)] [Find(LengthOf(Line(G,K)))]."
What is the measure of \angle B if m \angle A = 10?,"[Find(MeasureOf(Angle(B)))] if [Equals(MeasureOf(Angle(A)),10)]?"
Each pair of polygons is similar. Find x.,"[Similar(Polygon($1),Polygon($2))]. [Find(x)]."
EB \parallel DC. Find AB.,"[Parallel(Line(E,B),Line(D,C))]. [Find(LengthOf(Line(A,B)))]."
Use parallelogram ABCD to find m \angle DAB.,"Use [Parallelogram(A,B,C,D)] to [Find(MeasureOf(Angle(D,A,B)))]."
Find y.,[Find(y)].
Find x.,[Find(x)].
Quadrilateral ABCD is a rectangle. m \angle 2 = 40. Find m \angle 3.," [Rectangle(A,B,C,D)]. [Equals(MeasureOf(Angle(2)),40)] [Find(MeasureOf(Angle(3)))]."
Find KL.,"[Find(LengthOf(Line(K,L)))]."
Find y.,[Find(y)].
"In \odot R, find TV. Round to the nearest hundredth.","In [Circle(R)], [Find(LengthOf(Line(T,V)))]. Round to nearest hundredth."
"In \odot F, m \angle DFA = 50 and CF \perp FB. Find m \widehat ACE.","In [Circle(F)], [Equals(MeasureOf(Angle(D,F,A)),50)] and [Perpendicular(Line(C,F),Line(F,B))]. [Find(MeasureOf(Arc(A,C,E)))]."
Find the measure of m \angle 1. Assume that segments that appear tangent are tangent.,"[Find(MeasureOf(Angle(1)))]. [Tangent(Line($),Circle($))]."
MN \parallel BC. Solve for x.,"[Parallel(Line(M,N),Line(B,C))]. [Find(x)]."
The perimeter of this polygon is 60 centimeters. Find the length of the side of the polygon.,"[Equals(PerimeterOf(Polygon($)),60)] [Find(LengthOf(SideOf(Polygon($))))]."
"m \angle 2 = 2x, m \angle 3 = x. Find m \angle 2.","[Equals(MeasureOf(Angle(2)),2x)] [Equals(MeasureOf(Angle(3)),x)] [Find(MeasureOf(Angle(2)))]."
"The diagram shows the layout of Elm, Plum, and Oak streets. Find the value of x.","diagram shows layout of Elm, Plum and Oak streets. [Find(x)]."
Find m \angle 4.,[Find(MeasureOf(Angle(4)))].
Find y.,[Find(y)].
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find PQ.,"[Find(LengthOf(Line(P,Q)))]."
Find the variable of x to the nearest tenth. Assume that segments that appear to be tangent are tangent.,"[Find(x)] to nearest tenth. [Tangent(Line($),Circle($))]."
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
Find m \angle ABC.,"[Find(MeasureOf(Angle(A,B,C)))]."
"The diameters of \odot A, \odot B, and \odot C are 10, 30 and 10 units, respectively. Find AC if AZ \cong CW and CW = 2.","[Equals(DiameterOf(Circle(A)),10)] [Equals(DiameterOf(Circle(B)),30)] [Equals(DiameterOf(Circle(C)),10)] [Find(LengthOf(Line(A,C)))] if [Equals(LengthOf(Line(A,Z)),Line(C,W))] and [Equals(LengthOf(Line(C,W)),2)]."
Find the value of t in the parallelogram.,[Find(t)] in [Parallelogram($)].
Find the perimeter of the figure. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Shape($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
Find QS.,"[Find(LengthOf(Line(Q,S)))]."
Find x.,[Find(x)].
Find x.,[Find(x)].
Use parallelogram MNPR to find m \angle MNP.,"Use [Parallelogram(M,N,P,R)] to [Find(MeasureOf(Angle(M,N,P)))]."
Find m \widehat LP.,"[Find(MeasureOf(Arc(L,P)))]."
Find the length of AC in the isosceles triangle ABC.,"[Find(LengthOf(Line(A,C)))] in [Isosceles(Triangle(A,B,C))]."
"If AB \parallel DC, find x.","If [Parallel(Line(A,B),Line(D,C))], [Find(x)]."
WTY \cong TWY. Find x.,"[Congruent(Triangle(W,T,Y),Triangle(T,W,Y))]. [Find(x)]."
"In \odot X, AB = 30, CD = 30, and m \widehat CZ = 40. Find ND.","In [Circle(X)], [Equals(LengthOf(Line(A,B)),30)] [Equals(LengthOf(Line(C,D)),30)] and [Equals(MeasureOf(Arc(C,Z)),40)] [Find(LengthOf(Line(N,D)))]."
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Use parallelogram WXYZ to find m \angle XYZ.,"Use [Parallelogram(W,X,Y,Z)] to [Find(MeasureOf(Angle(X,Y,Z)))]."
"In \triangle PQR, ZQ = 3a-11, ZP = a+5, PY = 2c-1, YR = 4c-11, m \angle PRZ = 4b-17, m \angle ZRQ = 3b-4, m \angle QYR = 7b+6, and m \angle PXR = 2a+10. If RZ is an angle bisector, find m \angle PRZ.","In [Triangle(P,Q,R)], [Equals(LengthOf(Line(Z,Q)),3a-11)] [Equals(LengthOf(Line(Z,P)),a+5)] [Equals(LengthOf(Line(P,Y)),2c-1)] [Equals(LengthOf(Line(Y,R)),4c-11)] [Equals(MeasureOf(Angle(P,R,Z)),4b-17)] [Equals(MeasureOf(Angle(Z,R,Q)),3b-4)] [Equals(MeasureOf(Angle(Q,Y,R)),7b+6)] and [Equals(MeasureOf(Angle(P,X,R)),2a+10)] If [BisectsAngle(Line(R,Z),Angle($))], [Find(MeasureOf(Angle(P,R,Z)))]."
Find x.,[Find(x)].
Find x. A = 357 in^2.,"[Find(x)]. [Equals(AreaOf(Shape(A)),357)]."
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
Find x.,[Find(x)].
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
"Circle J has a radius of 10 units, \odot K has a radius of 8 units, and BC = 5.4 units. Find CK.","[Equals(RadiusOf(Circle(J)),10)] [Equals(RadiusOf(Circle(K)),8)] and [Equals(LengthOf(Line(B,C)),5.4)] [Find(LengthOf(Line(C,K)))]."
Quadrilateral WXYZ is a rectangle. Find the measure of \angle 5 if m \angle 1 = 30.," [Rectangle(W,X,Y,Z)]. [Find(MeasureOf(Angle(5)))] if [Equals(MeasureOf(Angle(1)),30)]."
Find y.,[Find(y)].
"If DB = 24, AE = 3, and EC = 18, find AD.","If [Equals(LengthOf(Line(D,B)),24)] [Equals(LengthOf(Line(A,E)),3)] and [Equals(LengthOf(Line(E,C)),18)] [Find(LengthOf(Line(A,D)))]."
Use parallelogram ABCD to find m \angle CDF.,"Use [Parallelogram(A,B,C,D)] to [Find(MeasureOf(Angle(C,D,F)))]."
Find m \angle B.,[Find(MeasureOf(Angle(B)))].
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Find x.,[Find(x)].
"In the figure, m \angle 3 = 43. Find the measure of \angle 11.",", [Equals(MeasureOf(Angle(3)),43)] [Find(MeasureOf(Angle(11)))]."
Find the measure of \angle 1.,[Find(MeasureOf(Angle(1)))].
Refer to the figure at the right. Find the value of m \angle FCE if p \parallel q.,"[Shape($)]. [Find(MeasureOf(Angle(F,C,E)))] if [Parallel(Line(p),Line(q))]."
"Use rectangle LMNP, parallelogram LKMJ to solve the problem. If LN = 10, LJ = 2x+1, and PJ = 3x-1, find x.","Use [Rectangle(L,M,N,P)], [Parallelogram(L,K,M,J)] to. If [Equals(LengthOf(Line(L,N)),10)] [Equals(LengthOf(Line(L,J)),2x+1)] and [Equals(LengthOf(Line(P,J)),3x-1)] [Find(x)]."
"If PR \parallel KL, KN = 9, LN = 16, and PM = 2KP, find KM.","If [Parallel(Line(P,R),Line(K,L))], [Equals(LengthOf(Line(K,N)),9)] [Equals(LengthOf(Line(L,N)),16)] and [Equals(LengthOf(Line(P,M)),Mul(Line(K,P),2))], [Find(LengthOf(Line(K,M)))]."
Each pair of polygons is similar. Find y.,"[Similar(Polygon($1),Polygon($2))]. [Find(y)]."
Find z.,[Find(z)].
\triangle LMN \cong \triangle QRS. Find x.,"[Congruent(Triangle(L,M,N),Triangle(Q,R,S))]. [Find(x)]."
"The diameters of \odot A, \odot B, and \odot C are 10, 30 and 10 units, respectively. Find YW if AZ \cong CW and CW = 2.","[Equals(DiameterOf(Circle(A)),10)] [Equals(DiameterOf(Circle(B)),30)] [Equals(DiameterOf(Circle(C)),10)] [Find(LengthOf(Line(Y,W)))] if [Equals(LengthOf(Line(A,Z)),Line(C,W))] and [Equals(LengthOf(Line(C,W)),2)]."
Find x.,[Find(x)].
Find the measure of \angle Z to the nearest tenth.,[Find(MeasureOf(Angle(Z)))] to nearest tenth.
Find the area of the shaded region formed by the circle and regular polygon. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))] formed by [Circle($)] and [Regular(Polygon($))]. Round to nearest tenth.
Use parallelogram MNPR to find x.,"Use [Parallelogram(M,N,P,R)] to [Find(x)]."
Each pair of polygons is similar. Find GF.,"[Similar(Polygon($1),Polygon($2))]. [Find(LengthOf(Line(G,F)))]."
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
A square is inscribed in a circle having a radius of 6 inches. Find the length of the side of the square.,"[InscribedIn(Square($),Circle($))], [Equals(RadiusOf(Circle($)),6)] [Find(LengthOf(SideOf(Square($))))]."
Find y.,[Find(y)].
Find x.,[Find(x)].
Find the area of the trapezoid.,[Find(AreaOf(Trapezoid($)))].
The segment is tangent to the circle. Find the value of x.,"[Tangent(Line($),Circle($))] to [Circle($)]. [Find(x)]."
Find x. Round to the nearest hundredth.,[Find(x)]. Round to nearest hundredth.
Express the ratio of \tan L as a decimal to the nearest hundredth.,[Find(RatioOf(TanOf(Angle(L))))] to nearest hundredth.
Find the area of the parallelogram.,[Find(AreaOf(Parallelogram($)))].
"In \odot S, m \widehat PQR = 98. Find m \widehat PQ.","In [Circle(S)], [Equals(MeasureOf(Arc(P,Q,R)),98)] [Find(MeasureOf(Arc(P,Q)))]."
Equilateral pentagon PQRST is inscribed in \odot U. Find m \angle PSR.,"[InscribedIn(Equilateral(Pentagon(P,Q,R,S,T)),Circle(U))]. [Find(MeasureOf(Angle(P,S,R)))]."
Find y.,[Find(y)].
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Find m \angle ABC if m \angle CDA = 61.,"[Find(MeasureOf(Angle(A,B,C)))] if [Equals(MeasureOf(Angle(C,D,A)),61)]."
ABCD is a parallelogram with side lengths as indicated in the figure at the right. The perimeter of ABCD is 22. Find AB.," [Parallelogram(A,B,C,D)]. [Equals(PerimeterOf(Quadrilateral(A,B,C,D)),22)] [Find(LengthOf(Line(A,B)))]."
Find AB.,"[Find(LengthOf(Line(A,B)))]."
"Find the area of the figure. Round to the nearest hundredth, if necessary.","[Find(AreaOf(Shape($)))]. Round to nearest hundredth, if necessary."
Which of the following facts would be sufficient to prove that line d is parallel to XZ?,"Which of following facts would be sufficient to prove [Parallel(Line(d),Line(X,Z))]?"
"If ZP = 4x-9 and PY = 2x+5, find ZX.","If [Equals(LengthOf(Line(Z,P)),4x-9)] and [Equals(LengthOf(Line(P,Y)),2x+5)] [Find(LengthOf(Line(Z,X)))]."
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
"If \frac{IJ}{XJ} = \frac{HJ}{YJ}, m \angle WXJ = 130 and m \angle WZG = 20, find m \angle YIZ.","If [Equals(RatioOf(Line(I,J),Line(X,J)),RatioOf(Line(H,J),Line(Y,J)))], [Equals(MeasureOf(Angle(W,X,J)),130)] and [Equals(MeasureOf(Angle(W,Z,G)),20)] [Find(MeasureOf(Angle(Y,I,Z)))]."
"In the figure, m \angle 1 = 50 and m \angle 3 = 60. Find the measure of \angle 6.",", [Equals(MeasureOf(Angle(1)),50)] and [Equals(MeasureOf(Angle(3)),60)] [Find(MeasureOf(Angle(6)))]."
Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.,"[Find(x)] to nearest tenth. [Tangent(Line($),Circle($))]."
Find the value of the variable x in the figure.,[Find(x)].
Find m \angle H.,[Find(MeasureOf(Angle(H)))].
"Find the perimeter of \triangle WZX, if \triangle WZX \sim \triangle SRT, ST = 6, WX = 5, and the perimeter of \triangle SRT = 15.","[Find(PerimeterOf(Triangle(W,Z,X)))], if [Similar(Triangle(W,Z,X),Triangle(S,R,T))], [Equals(LengthOf(Line(S,T)),6)] [Equals(LengthOf(Line(W,X)),5)] and [Equals(PerimeterOf(Triangle(S,R,T)),15)]."
"In the figure, m \angle 1 = 4p+15, m \angle 3 = 3p-10 and m \angle 4 = 6r+5. Find the value of p.",", [Equals(MeasureOf(Angle(1)),4p+15)] [Equals(MeasureOf(Angle(3)),3p-10)] and [Equals(MeasureOf(Angle(4)),6r+5)] [Find(p)]."
Trapezoid GHJK has an area of 75 square meters. Find the height.,"[Equals(AreaOf(Trapezoid(G,H,J,K)),75)] [Find(HeightOf(Polygon($)))]."
Find the area of \parallelogram JKLM.,"[Find(AreaOf(Parallelogram(J,K,L,M)))]."
"Circle A has diameters DF and PG. If DF = 10, find DA.","[IsDiameterOf(Line(D,F),Circle(A))], [IsDiameterOf(Line(P,G),Circle(A))]. If [Equals(LengthOf(Line(D,F)),10)] [Find(LengthOf(Line(D,A)))]."
Find x.,[Find(x)].
\triangle ABC \sim \triangle FDG. Find the value of x.,"[Similar(Triangle(A,B,C),Triangle(F,D,G))]. [Find(x)]."
"AC is a diagonal of rhombus ABCD. If m \angle CDE is 116, what is m \angle ACD?","[IsDiagonalOf(Line(A,C),Rhombus(A,B,C,D))]. If [Equals(MeasureOf(Angle(C,D,E)),116)] [Find(MeasureOf(Angle(A,C,D)))]?"
Find the value of the variable y in the figure.,[Find(y)].
Find the scale from B to B'.,"[Find(ScaleFactorOf(Shape(B),Shape(B')))]."
Find x.,[Find(x)].
Find the value of x.,[Find(x)].
"In the figure, m \angle 1 = 50 and m \angle 3 = 60. Find the measure of \angle 4.",", [Equals(MeasureOf(Angle(1)),50)] and [Equals(MeasureOf(Angle(3)),60)] [Find(MeasureOf(Angle(4)))]."
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Find m \angle A.,[Find(MeasureOf(Angle(A)))].
Solve for x in the figure. Round to the nearest tenth if necessary.,[Find(x)]. Round to nearest tenth if necessary.
Find m \widehat XZ.,"[Find(MeasureOf(Arc(X,Z)))]."
P is the incenter of \triangle AEC. Find m \angle DEP.,"[IsIncenterOf(Point(P),Triangle(A,E,C))]. [Find(MeasureOf(Angle(D,E,P)))]."
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Find x so that the quadrilateral is a parallelogram.,[Find(x)] so [Parallelogram($)]
Quadrilateral ABCD is a rectangle. m \angle 2 = 40. Find m \angle 8.," [Rectangle(A,B,C,D)]. [Equals(MeasureOf(Angle(2)),40)] [Find(MeasureOf(Angle(8)))]."
Find z.,[Find(z)].
Find x.,[Find(x)].
Find x.,[Find(x)].
Find \angle 9.,[Find(MeasureOf(Angle(9)))].
"If ABCD is a rhombus, and m \angle ABC = 70, what is m \angle 1?","If [Rhombus(A,B,C,D)] and [Equals(MeasureOf(Angle(A,B,C)),70)] [Find(MeasureOf(Angle(1)))]?"
Find x.,[Find(x)].
Find the length of \widehat JK. Round to the nearest hundredth.,"[Find(LengthOf(Arc(J,K)))]. Round to nearest hundredth."
Find x. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. [Tangent(Line($),Circle($))]."
Find x.,[Find(x)].
Find XW.,"[Find(LengthOf(Line(X,W)))]."
Find m \widehat QTS.,"[Find(MeasureOf(Arc(Q,T,S)))]."
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
"In \odot T, ZV = 1, and TW = 13. Find XY.","In [Circle(T)], [Equals(LengthOf(Line(Z,V)),1)] and [Equals(LengthOf(Line(T,W)),13)] [Find(LengthOf(Line(X,Y)))]."
"UJ = 9, VJ = 3, and ZT = 18. Find SV.","[Equals(LengthOf(Line(U,J)),9)] [Equals(LengthOf(Line(V,J)),3)] and [Equals(LengthOf(Line(Z,T)),18)] [Find(LengthOf(Line(S,V)))]."
"Find a, if FG = 18, GH = 42, and FK = 15.","[Find(a)], if [Equals(LengthOf(Line(F,G)),18)] [Equals(LengthOf(Line(G,H)),42)] and [Equals(LengthOf(Line(F,K)),15)]."
Find the measure of \angle 3 if m \angle 4 = m \angle 5.,"[Find(MeasureOf(Angle(3)))] if [Equals(MeasureOf(Angle(4)),MeasureOf(Angle(5)))]."
Find y so that the quadrilateral is a parallelogram.,[Find(y)] so [Parallelogram($)]
"For the pair of similar figures, use the given areas to find the scale factor from the blue to the green figure.","[Similar(Shape($1),Shape($2))], to [Find(ScaleFactorOf(Blue(Shape($)),Green(Shape($))))]."
Find m \angle Z.,[Find(MeasureOf(Angle(Z)))].
Find the measure of m \widehat YXZ.,"[Find(MeasureOf(Arc(Y,X,Z)))]."
"If RL = 5, RT = 9, and WS = 6, find RW.","If [Equals(LengthOf(Line(R,L)),5)] [Equals(LengthOf(Line(R,T)),9)] and [Equals(LengthOf(Line(W,S)),6)] [Find(LengthOf(Line(R,W)))]."
Find the area of the shaded region. Assume that the polygon is regular unless otherwise stated. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. [Regular(Polygon($))]. Round to nearest tenth.
"Chords AC and DF are equidistant from the center. If the radius of \odot G is 26, find AC.","[IsChordOf(Line(A,C),Circle($))], [IsChordOf(Line(D,F),Circle($))]. [Line(A,C)] and [Line(D,F)] are equidistant from center. If [Equals(RadiusOf(Circle(G)),26)] [Find(LengthOf(Line(A,C)))]."
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Use parallelogram ABCD to find m \angle ACD.,"Use [Parallelogram(A,B,C,D)] to [Find(MeasureOf(Angle(A,C,D)))]."
Find m \angle CAD.,"[Find(MeasureOf(Angle(C,A,D)))]."
Find x. Round to the nearest hundredth.,[Find(x)]. Round to nearest hundredth.
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
"In \odot O, EC and AB are diameters, and \angle BOD \cong \angle DOE \cong \angle EOF \cong \angle FOA. Find m \widehat AE.","[Circle(O)], [IsDiameterOf(Line(E,C),Circle(O))], [IsDiameterOf(Line(A,B),Circle(O))] and [Equals(Angle(B,O,D),Angle(D,O,E))], [Equals(Angle(D,O,E),Angle(E,O,F))], [Equals(Angle(E,O,F),Angle(F,O,A))]. [Find(MeasureOf(Arc(A,E)))]."
Find \angle C of quadrilateral ABCD.,"[Find(MeasureOf(Angle(C)))] of [Quadrilateral(A,B,C,D)]."
Find x.,[Find(x)].
Find x so that BE and AD are perpendicular.,"[Find(x)] so [Perpendicular(Line(B,E),Line(A,D))]."
The ratio of the measure of the angles of the triangle below is 3 : 2 : 1. Which of the following is not an angle measure of the triangle?,"ratio of measure of angles of [Equals(Triangle($),3)] : 2 : 1. Which of following is not angle [LengthOf(Triangle($))]?"
"Quadrilateral ABDC is a rectangle. If m \angle 1 = 38, find m \angle 2."," [Rectangle(A,B,D,C)]. If [Equals(MeasureOf(Angle(1)),38)] [Find(MeasureOf(Angle(2)))]."
Find x.,[Find(x)].
Quadrilateral WXYZ is inscribed in \odot V. Find m \angle X.,"[InscribedIn(Quadrilateral(W,X,Y,Z),Circle(V))]. [Find(MeasureOf(Angle(X)))]."
Find DE.,"[Find(LengthOf(Line(D,E)))]."
"If WXYZ is a kite, find WP.","If [Kite(W,X,Y,Z)], [Find(LengthOf(Line(W,P)))]."
"If two sides of a triangle measure 12 and 7, which of the following cannot be the perimeter of the triangle?","If two sides of [Triangle($)] measure 12 and 7, which of following cannot be [PerimeterOf(Triangle($))]?"
"In RSTV, RS = 6, VT = 3 and RX is twice the length of XV. Find XY.","In [Quadrilateral(R,S,T,V)], [Equals(LengthOf(Line(R,S)),6)] [Equals(LengthOf(Line(V,T)),3)] and [Equals(Line(R,X),Mul(LengthOf(Line(X,V)),2))]. [Find(LengthOf(Line(X,Y)))]."
Find the area of the triangle. Round to the nearest tenth if necessary.,[Find(AreaOf(Triangle($)))]. Round to nearest tenth if necessary.
Find x.,[Find(x)].
Find the area of the rhombus.,[Find(AreaOf(Rhombus($)))].
Find the area of the figure. Round to the nearest tenth.,[Find(AreaOf(Shape($)))]. Round to nearest tenth.
"Quadrilateral ABCD is a rhombus. If AB = 2x+3 and BC = x+7, find CD."," [Rhombus(A,B,C,D)]. If [Equals(LengthOf(Line(A,B)),2x+3)] and [Equals(LengthOf(Line(B,C)),x+7)] [Find(LengthOf(Line(C,D)))]."
"For trapezoid TRSV, M and N are midpoints of the legs. If TR = 32 and MN = 25, find VS.","[Trapezoid(T,R,S,V)], [IsMidpointOf(Point(M),LegOf(Trapezoid(T,R,S,V)))], [IsMidpointOf(Point(N),LegOf(Trapezoid(T,R,S,V)))],. If [Equals(LengthOf(Line(T,R)),32)] and [Equals(LengthOf(Line(M,N)),25)] [Find(LengthOf(Line(V,S)))]."
The segment is tangent to the circle. Find x. Round to the nearest tenth.,"[Tangent(Line($),Circle($))] to [Circle($)]. [Find(x)]. Round to nearest tenth."
"MC = 7, RM = 4, and AT = 16. Find MS.","[Equals(LengthOf(Line(M,C)),7)] [Equals(LengthOf(Line(R,M)),4)] and [Equals(LengthOf(Line(A,T)),16)] [Find(LengthOf(Line(M,S)))]."
"In \odot P, JK = 10 and \widehat JKL = 134. Find m \widehat JL.","In [Circle(P)], [Equals(LengthOf(Line(J,K)),10)] and [Equals(Arc(J,K,L),134)] [Find(MeasureOf(Arc(J,L)))]."
Quadrilateral WXYZ is a rectangle. Find the measure of \angle 3 if m \angle 1 = 30.," [Rectangle(W,X,Y,Z)]. [Find(MeasureOf(Angle(3)))] if [Equals(MeasureOf(Angle(1)),30)]."
"In rhombus ABCD, m \angle DAB = 2, m \angle ADC and CB = 6. Find m \angle ADB.","In [Rhombus(A,B,C,D)], [Equals(MeasureOf(Angle(D,A,B)),2)] [MeasureOf(Angle(A,D,C))] and [Equals(LengthOf(Line(C,B)),6)] [Find(MeasureOf(Angle(A,D,B)))]."
\triangle JKL \sim \triangle WYZ. Find x.,"[Similar(Triangle(J,K,L),Triangle(W,Y,Z))]. [Find(x)]."
Find the area of the shaded region. Assume that the polygon is regular unless otherwise stated. Round to the nearest tenth.,[Find(AreaOf(Shaded(Shape($))))]. [Regular(Polygon($))]. Round to nearest tenth.
Find x.,[Find(x)].
Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.,"[Find(x)] to nearest tenth. [Tangent(Line($),Circle($))]."
Find m \angle 3.,[Find(MeasureOf(Angle(3)))].
"In \triangle CDF, K is the centroid and DK = 16. Find CD."," [Triangle(C,D,F)], [IsCentroidOf(Point(K),Triangle(C,D,F))] and [Equals(LengthOf(Line(D,K)),16)] [Find(LengthOf(Line(C,D)))]."
Find z.,[Find(z)].
A square is inscribed in a circle of area 18\pi square units. Find the length of a side of the square.,"[InscribedIn(Square($),Circle($))], [Equals(AreaOf(Square($)),18\pi)] [Find(LengthOf(SideOf(Square($))))]."
"Circles G, J, and K all intersect at L. If GH = 10, find the measure. Find JL.","[IntersectAt(Circle(G),Circle(J),Circle(K),Point(L))]. If [Equals(LengthOf(Line(G,H)),10)] [Find(LengthOf(Line(J,L)))]."
Find a in the given parallelogram.,[Find(a)] in [Parallelogram($)].
"If PR \parallel KL, KN = 9, LN = 16, PM = 2 KP, find PR.","If [Parallel(Line(P,R),Line(K,L))], [Equals(LengthOf(Line(K,N)),9)] [Equals(LengthOf(Line(L,N)),16)] [Equals(LengthOf(Line(P,M)),Mul(Line(K,P),2))], [Find(LengthOf(Line(P,R)))]."
The area A of the shaded region is given. Find x. A = 66 cm^2.,". [Find(x)]. [Equals(AreaOf(Shape(A)),66)]."
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Express the ratio of \cos A as a decimal to the nearest hundredth.,[Find(RatioOf(CosOf(Angle(A))))] to nearest hundredth.
Use parallelogram ABCD to find m \angle DAC.,"Use [Parallelogram(A,B,C,D)] to [Find(MeasureOf(Angle(D,A,C)))]."
\triangle LMN \cong \triangle QRS. Find x.,"[Congruent(Triangle(L,M,N),Triangle(Q,R,S))]. [Find(x)]."
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
"In the figure, m \angle 1 = 58, m \angle 2 = 47, and m \angle 3 = 26. Find the measure of \angle 9.",", [Equals(MeasureOf(Angle(1)),58)] [Equals(MeasureOf(Angle(2)),47)] and [Equals(MeasureOf(Angle(3)),26)] [Find(MeasureOf(Angle(9)))]."
Find y.,[Find(y)].
Find m \widehat JKL.,"[Find(MeasureOf(Arc(J,K,L)))]."
Find y.,[Find(y)].
m \angle 4 = 2y+32 and m \angle 5 = 3y-3. Find y.,"[Equals(MeasureOf(Angle(4)),2y+32)] and [Equals(MeasureOf(Angle(5)),3y-3)] [Find(y)]."
"Quadrilateral EFGH is a rectangle. If EF = 4x-6 and HG = x+3, find EF."," [Rectangle(E,F,G,H)]. If [Equals(LengthOf(Line(E,F)),4x-6)] and [Equals(LengthOf(Line(H,G)),x+3)] [Find(LengthOf(Line(E,F)))]."
Find x.,[Find(x)].
Find AB.,"[Find(LengthOf(Line(A,B)))]."
"a = 14, b = 48, and c = 50, find \cos A.","[Equals(a,14)] [Equals(b,48)] and [Equals(c,50)] [Find(CosOf(Angle(A)))]."
Find h in the triangle.,[Find(h)] in [Triangle($)].
Find y.,[Find(y)].
The segment is tangent to the circle. Find x.,"[Tangent(Line($),Circle($))] to [Circle($)]. [Find(x)]."
Find GH in the kite.,"[Find(LengthOf(Line(G,H)))] in [Kite($)]."
Find x in the figure.,[Find(x)].
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.,[Find(PerimeterOf(Parallelogram($)))]. Round to nearest tenth if necessary.
Find the value of the variable t.,[Find(t)].
"In the figure, line l is parallel to line m. Line n intersects both l and m. Which of the following lists includes all of the angles that are supplementary to \angle 1?",", [Parallel(Line(l),Line(m))]. [IntersectAt(Line(n),Line(l),Point($))], [IntersectAt(Line(n),Line(m),Point($))]. Which of following lists includes of angles are supplementary to [Angle(1)]?"
Find m \angle W.,[Find(MeasureOf(Angle(W)))].
Find the measure of \angle 7 if m \angle 4 = m \angle 5.,"[Find(MeasureOf(Angle(7)))] if [Equals(MeasureOf(Angle(4)),MeasureOf(Angle(5)))]."
Express the ratio of \cos N as a decimal to the nearest hundredth.,[Find(RatioOf(CosOf(Angle(N))))] to nearest hundredth.
Use parallelogram ABCD to find AD.,"Use [Parallelogram(A,B,C,D)] to [Find(LengthOf(Line(A,D)))]."
"In the figure, m \angle 3 = 110 and m \angle 12 = 55. Find the measure of \angle 13.",", [Equals(MeasureOf(Angle(3)),110)] and [Equals(MeasureOf(Angle(12)),55)] [Find(MeasureOf(Angle(13)))]."
AD and CG are diameters of \odot B. Find m \widehat AG.,"[IsDiameterOf(Line(A,D),Circle(B))], [IsDiameterOf(Line(C,G),Circle(B))]. [Find(MeasureOf(Arc(A,G)))]."
Find x.,[Find(x)].
Find x. A = 148m^2.,"[Find(x)]. [Equals(AreaOf(Shape(A)),148)]."
Find the measure of \angle 2.,[Find(MeasureOf(Angle(2)))].
Find the area of the kite.,[Find(AreaOf(Kite($)))].
Find the measure of m \angle 1.,[Find(MeasureOf(Angle(1)))].
Find y.,[Find(y)].
"If PR \parallel KL, KN = 9, LN = 16, PM = 2 KP, find MN.","If [Parallel(Line(P,R),Line(K,L))], [Equals(LengthOf(Line(K,N)),9)] [Equals(LengthOf(Line(L,N)),16)] [Equals(LengthOf(Line(P,M)),Mul(Line(K,P),2))], [Find(LengthOf(Line(M,N)))]."
Find PS.,"[Find(LengthOf(Line(P,S)))]."
"Find the perimeter of \triangle DEF, if \triangle DEF \sim \triangle CBF, perimeter of \triangle CBF = 27, DF = 6, and FC = 8.","[Find(PerimeterOf(Triangle(D,E,F)))], if [Similar(Triangle(D,E,F),Triangle(C,B,F))], [Equals(PerimeterOf(Triangle(C,B,F)),27)] [Equals(LengthOf(Line(D,F)),6)] and [Equals(LengthOf(Line(F,C)),8)]."
Find the area of the regular polygon figure. Round to the nearest tenth.,[Find(AreaOf(Regular(Polygon($))))]. Round to nearest tenth.
\angle 1 and \angle 2 form a linear pair and m \angle 2 = 67. Find the measure of \angle 1.,"[Equals(SumOf(MeasureOf(Angle(1)),MeasureOf(Angle(1))),180)] and [Equals(MeasureOf(Angle(2)),67)] [Find(MeasureOf(Angle(1)))]."
Find x.,[Find(x)].
"In \odot P, m \angle MPL = 65 and NP \perp PL. Find m \widehat NJK.","In [Circle(P)], [Equals(MeasureOf(Angle(M,P,L)),65)] and [Perpendicular(Line(N,P),Line(P,L))]. [Find(MeasureOf(Arc(N,J,K)))]."
Find EG if G is the incenter of \triangle ABC.,"[Find(LengthOf(Line(E,G)))] if [IsIncenterOf(Point(G),Triangle(A,B,C))]."
GH \cong KJ. Find x.,"[Equals(LengthOf(Line(G,H)),Line(K,J))]. [Find(x)]."
Find m \angle 3.,[Find(MeasureOf(Angle(3)))].
"Find BC if AB = 6, AF = 8, BC = x, CD = y, DE = 2y-3, and FE = x+\frac{10}{3}.","[Find(LengthOf(Line(B,C)))] if [Equals(LengthOf(Line(A,B)),6)] [Equals(LengthOf(Line(A,F)),8)] [Equals(LengthOf(Line(B,C)),x)] [Equals(LengthOf(Line(C,D)),y)] [Equals(LengthOf(Line(D,E)),2y-3)] and [Equals(LengthOf(Line(F,E)),x+\frac{10}{3})]."
"If pentagons ABCDE and PQRST are similar, find SR.","If [Similar(Pentagon(A,B,C,D,E),Pentagon(P,Q,R,S,T))], [Find(LengthOf(Line(S,R)))]."
Find m \angle D.,[Find(MeasureOf(Angle(D)))].
"In \odot F, FH \cong FL and FK = 17. Find JG.","In [Circle(F)], [Equals(LengthOf(Line(F,H)),Line(F,L))] and [Equals(LengthOf(Line(F,K)),17)] [Find(LengthOf(Line(J,G)))]."
Find x.,[Find(x)].
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
Find PT.,"[Find(LengthOf(Line(P,T)))]."
"In \odot B, CE = 13.5. Find BD. Round to the nearest hundredth.","In [Circle(B)], [Equals(LengthOf(Line(C,E)),13.5)] [Find(LengthOf(Line(B,D)))]. Round to nearest hundredth."
"in \triangle XYZ, P is the centroid, KP = 3, and XJ = 8. Find YJ.","in  [Triangle(X,Y,Z)], [IsCentroidOf(Point(P),Triangle(X,Y,Z))], [Equals(LengthOf(Line(K,P)),3)] and [Equals(LengthOf(Line(X,J)),8)] [Find(LengthOf(Line(Y,J)))]."
Express the ratio of \cos P as a decimal to the nearest hundredth.,[Find(RatioOf(CosOf(Angle(P))))] to nearest hundredth.
Find the perimeter of the parallelogram.,[Find(PerimeterOf(Parallelogram($)))].
Find z.,[Find(z)].
Use parallelogram JKLM to find m \angle JML.,"Use [Parallelogram(J,K,L,M)] to [Find(MeasureOf(Angle(J,M,L)))]."
Find x in the given parallelogram.,[Find(x)] in [Parallelogram($)].
Find the area of the figure to the nearest tenth.,[Find(AreaOf(Shape($)))] to nearest tenth.
"If CW = WF and ED = 30, what is DF?","If [Equals(LengthOf(Line(C,W)),Line(W,F))] and [Equals(LengthOf(Line(E,D)),30)] [Find(LengthOf(Line(D,F)))]?"
Find the area of the triangle. Round to the nearest hundredth.,[Find(AreaOf(Triangle($)))]. Round to nearest hundredth.
\triangle WXY \cong \triangle WXZ. Find y.,"[Congruent(Triangle(W,X,Y),Triangle(W,X,Z))]. [Find(y)]."
Find the measure of JK.,"[Find(LengthOf(Line(J,K)))]."
Express the ratio of \sin N as a decimal to the nearest hundredth.,[Find(RatioOf(SinOf(Angle(N))))] to nearest hundredth.
Use the Pythagorean Theorem to find the length of the hypotenuse of the right triangle.,[UseTheorem(Pythagorean_Theorem)] to [Find(LengthOf(HypotenuseOf(Right(Triangle($)))))].
"Find y. Round to the nearest tenth, if necessary.","[Find(y)]. Round to nearest tenth, if necessary."
Quadrilateral ABCD is a rectangle. Find x.," [Rectangle(A,B,C,D)]. [Find(x)]."
Find m \angle JKL.,"[Find(MeasureOf(Angle(J,K,L)))]."
Find y.,[Find(y)].
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
Find x.,[Find(x)].
"If c = 5, find b.","If [Equals(c,5)] [Find(b)]."
"In the figure, m \angle 12 = 64. Find the measure of \angle 7.",", [Equals(MeasureOf(Angle(12)),64)] [Find(MeasureOf(Angle(7)))]."
Find x.,[Find(x)].
Find the area of the parallelogram. Round to the nearest tenth if necessary.,[Find(AreaOf(Parallelogram($)))]. Round to nearest tenth if necessary.
"In \odot O, EC and AB are diameters, and \angle BOD \cong \angle DOE \cong \angle EOF \cong \angle FOA. Find m \widehat AD.","[Circle(O)], [IsDiameterOf(Line(E,C),Circle(O))], [IsDiameterOf(Line(A,B),Circle(O))] and [Equals(Angle(B,O,D),Angle(D,O,E))], [Equals(Angle(D,O,E),Angle(E,O,F))], [Equals(Angle(E,O,F),Angle(F,O,A))]. [Find(MeasureOf(Arc(A,D)))]."
Find KL.,"[Find(LengthOf(Line(K,L)))]."
Find TQ.,"[Find(LengthOf(Line(T,Q)))]."
"Find x so that GJ \parallel FK. GH = x+3.5, HJ = x-8.5, FH = 21, HK = 7.","[Find(x)] so [Parallel(Line(G,J),Line(F,K))]. [Equals(LengthOf(Line(G,H)),x+3.5)] [Equals(LengthOf(Line(H,J)),x-8.5)] [Equals(LengthOf(Line(F,H)),21)] [Equals(LengthOf(Line(H,K)),7)]."
"One diagonal of a rhombus is twice as long as the other diagonal. If the area of the rhombus is 169 square millimeters, what are the lengths of the diagonals?","One diagonal of [Equals(Rhombus($),2long)] other diagonal. If [Equals(AreaOf(Rhombus($)),169)] what are lengths of diagonals?"
"For trapezoid QRTU, V and S are midpoints of the legs. If QR = 4 and UT = 16, find VS.","[Trapezoid(Q,R,T,U)], [IsMidpointOf(Point(V),LegOf(Trapezoid(Q,R,T,U)))], [IsMidpointOf(Point(S),LegOf(Trapezoid(Q,R,T,U)))],. If [Equals(LengthOf(Line(Q,R)),4)] and [Equals(LengthOf(Line(U,T)),16)] [Find(LengthOf(Line(V,S)))]."
Find the measure of \angle T to the nearest tenth.,[Find(MeasureOf(Angle(T)))] to nearest tenth.
Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.,"[Find(x)]. Round to nearest tenth if necessary. [Tangent(Line($),Circle($))]."
Find x.,[Find(x)].
Find \cos C.,[Find(CosOf(Angle(C)))].
Find the area of the figure.,[Find(AreaOf(Shape($)))].
Find the area of the trapezoid.,[Find(AreaOf(Trapezoid($)))].
"The area of trapezoid JKLM is 138 square feet. The area of trapezoid QRST is 5.52 square feet. If trapezoid JKLM \sim trapezoid QRST, find the value of x.","[Equals(AreaOf(Trapezoid(J,K,L,M)),138)] [Equals(AreaOf(Trapezoid(Q,R,S,T)),5.52)] If [Similar(Trapezoid(J,K,L,M),Trapezoid(Q,R,S,T))], [Find(x)]."
"Find CF if BF bisects \angle ABC and AC \parallel ED, BA = 6, BC = 7.5, AC = 9, and DE = 9.","[Find(LengthOf(Line(C,F)))] if [BisectsAngle(Line(B,F),Angle(A,B,C))] and [Parallel(Line(A,C),Line(E,D))], [Equals(LengthOf(Line(B,A)),6)] [Equals(LengthOf(Line(B,C)),7.5)] [Equals(LengthOf(Line(A,C)),9)] and [Equals(LengthOf(Line(D,E)),9)]."
"If \frac{IJ}{XJ} = \frac{HJ}{YJ}, m \angle WXJ = 130 and m \angle WZG = 20, find m \angle J.","If [Equals(RatioOf(Line(I,J),Line(X,J)),RatioOf(Line(H,J),Line(Y,J)))], [Equals(MeasureOf(Angle(W,X,J)),130)] and [Equals(MeasureOf(Angle(W,Z,G)),20)] [Find(MeasureOf(Angle(J)))]."
Use a calculator to find the measure of \angle J to the nearest degree.,to [Find(MeasureOf(Angle(J)))] to nearest degree.
Find w in the given parallelogram.,[Find(w)] in [Parallelogram($)].
"For trapezoid ABCD, S and T are midpoints of the legs. If CD = 14, ST = 10, and AB = 2x, find x.","[Trapezoid(A,B,C,D)], [IsMidpointOf(Point(S),LegOf(Trapezoid(A,B,C,D)))], [IsMidpointOf(Point(T),LegOf(Trapezoid(A,B,C,D)))],. If [Equals(LengthOf(Line(C,D)),14)] [Equals(LengthOf(Line(S,T)),10)] and [Equals(LengthOf(Line(A,B)),2x)] [Find(x)]."
Find m \angle 1.,[Find(MeasureOf(Angle(1)))].
Find y.,[Find(y)].
"Find the area of the figure in feet. Round to the nearest tenth, if necessary.","[Find(AreaOf(Shape($)))] in. Round to nearest tenth, if necessary."
Express the ratio of \tan M as a decimal to the nearest hundredth.,[Find(RatioOf(TanOf(Angle(M))))] to nearest hundredth.
Find x.,[Find(x)].
Find the value of x in the diagram.,[Find(x)].
Find x.,[Find(x)].
"In \odot X, AB = 30, CD = 30, and m \widehat CZ = 40. Find m \widehat CD.","In [Circle(X)], [Equals(LengthOf(Line(A,B)),30)] [Equals(LengthOf(Line(C,D)),30)] and [Equals(MeasureOf(Arc(C,Z)),40)] [Find(MeasureOf(Arc(C,D)))]."
"In the figure, square ABDC is inscribed in \odot K. Find the measure of a central angle.",", [InscribedIn(Square(A,B,D,C),Circle(K))]. [Find(MeasureOf(Angle($)))]."
Find BC.,"[Find(LengthOf(Line(B,C)))]."
Use parallelogram ABCD to find m \angle AFD.,"Use [Parallelogram(A,B,C,D)] to [Find(MeasureOf(Angle(A,F,D)))]."
Quadrilateral WXYZ is a rectangle. Find the measure of \angle 2 if m \angle 1 = 30.," [Rectangle(W,X,Y,Z)]. [Find(MeasureOf(Angle(2)))] if [Equals(MeasureOf(Angle(1)),30)]."
Find m \angle H.,[Find(MeasureOf(Angle(H)))].
"If FGHJ is a kite, find m \angle GFJ.","If [Kite(F,G,H,J)], [Find(MeasureOf(Angle(G,F,J)))]."
Find x.,[Find(x)].
"In the figure, AD is perpendicular to BC and AB is perpendicular to AC. What is BC?",", [Perpendicular(Line(A,D),Line(B,C))] and [Perpendicular(Line(A,B),Line(A,C))]. [Find(LengthOf(Line(B,C)))]?"
Find the area of the figure. Round to the nearest tenth if necessary.,[Find(AreaOf(Shape($)))]. Round to nearest tenth if necessary.
Point D is the center of the circle. What is m \angle ABC?,"[IsCentroidOf(Point(D),Circle($))]. [Find(MeasureOf(Angle(A,B,C)))]?"
Find the perimeter of the figure.,[Find(PerimeterOf(Shape($)))].
"For trapezoid QRST, A and B are midpoints of the legs. Find m \angle S.","[Trapezoid(Q,R,S,T)], [IsMidpointOf(Point(A),LegOf(Trapezoid(Q,R,S,T)))], [IsMidpointOf(Point(B),LegOf(Trapezoid(Q,R,S,T)))],. [Find(MeasureOf(Angle(S)))]."
Find the measure of \angle 3.,[Find(MeasureOf(Angle(3)))].
Find m \angle 2.,[Find(MeasureOf(Angle(2)))].
"\angle 6 and \angle 8 are complementary, m \angle 8 = 47. Find the measure of \angle 7.","[Equals(SumOf(MeasureOf(Angle(6)),MeasureOf(Angle(6))),90)], [Equals(MeasureOf(Angle(8)),47)] [Find(MeasureOf(Angle(7)))]."
Find AB.,"[Find(LengthOf(Line(A,B)))]."
Find x.,[Find(x)].
Find z.,[Find(z)].
Find the area of the rhombus.,[Find(AreaOf(Rhombus($)))].
find \sin S.,[Find(SinOf(Angle(S)))].
Find JL.,"[Find(LengthOf(Line(J,L)))]."
Find the area of the shaded sector. Round to the nearest tenth.,[Find(AreaOf(Shaded(Sector($))))]. Round to nearest tenth.
"In the figure, CP is an altitude, CQ is the angle bisector of \angle ACB, and R is the midpoint of AB. Find m \angle ACQ if m \angle ACB = 123-x and m \angle QCB = 42+x.",", [IsAltitudeOf(Line(C,P),Shape($))], [BisectsAngle(Line(C,Q),Angle(A,C,B))] and [IsMidpointOf(Point(R),Line(A,B))]. [Find(MeasureOf(Angle(A,C,Q)))] if [Equals(MeasureOf(Angle(A,C,B)),123-x)] and [Equals(MeasureOf(Angle(Q,C,B)),42+x)]."
Find z.,[Find(z)].
Find x.,[Find(x)].
Find z in the given parallelogram.,[Find(z)] in [Parallelogram($)].
"If CE = t-2. EB = t+1, CD = 2, and CA = 10, find CE.","If [Equals(LengthOf(Line(C,E)),t-2)] [Equals(LengthOf(Line(E,B)),t+1)] [Equals(LengthOf(Line(C,D)),2)] and [Equals(LengthOf(Line(C,A)),10)] [Find(LengthOf(Line(C,E)))]."
"If c = 5, find a.","If [Equals(c,5)] [Find(a)]."
"The degree measure of minor arc \widehat AC and major arc \widehat ADC are x and y respectively. If m \angle ABC = 70, find x.","degree measure ofinor arc [Arc(A,C)] and major arc [Arc(A,D,C)] are x and y. If [Equals(MeasureOf(Angle(A,B,C)),70)] [Find(x)]."
Find m \angle WYZ.,"[Find(MeasureOf(Angle(W,Y,Z)))]."
Use parallelogram to find b.,Use [Parallelogram($)] to [Find(b)].
"UJ = 9, VJ = 3, and ZT = 18. Find SJ.","[Equals(LengthOf(Line(U,J)),9)] [Equals(LengthOf(Line(V,J)),3)] and [Equals(LengthOf(Line(Z,T)),18)] [Find(LengthOf(Line(S,J)))]."
Find AB.,"[Find(LengthOf(Line(A,B)))]."
PQRS is a rhombus inscribed in a circle. Find m \widehat SP.," [InscribedIn(Rhombus(P,Q,R,S),Circle($))]. [Find(MeasureOf(Arc(S,P)))]."
Tangent MP is drawn to \odot O. Find x if MO = 20.,"[Tangent(Line(M,P),Circle(O))]. [Find(x)] if [Equals(LengthOf(Line(M,O)),20)]."
Find the measure of \angle 2.,[Find(MeasureOf(Angle(2)))].
Find GD.,"[Find(LengthOf(Line(G,D)))]."
"In \odot P, m \angle MPL = 65 and NP \perp PL. Find m \widehat NM.","In [Circle(P)], [Equals(MeasureOf(Angle(M,P,L)),65)] and [Perpendicular(Line(N,P),Line(P,L))]. [Find(MeasureOf(Arc(N,M)))]."
Find the area of the regular polygon. Round to the nearest tenth.,[Find(AreaOf(Regular(Polygon($))))]. Round to nearest tenth.
Find the length of \widehat ZY. Round to the nearest hundredth.,"[Find(LengthOf(Arc(Z,Y)))]. Round to nearest hundredth."
Find the area of the rhombus.,[Find(AreaOf(Rhombus($)))].
m \angle 4 = 42. Find m \angle 7.,"[Equals(MeasureOf(Angle(4)),42)] [Find(MeasureOf(Angle(7)))]."
Cut four congruent triangles off the corners of a rectangle to make an octagon. What is the area of the octagon?,Cut four congruent triangles off corners of [Rectangle($)] to make [Octagon($)]. [Find(AreaOf(Octagon($)))]?
Find m \angle Y.,[Find(MeasureOf(Angle(Y)))].
Each pair of polygons is similar. Find AC.,"[Similar(Polygon($1),Polygon($2))]. [Find(LengthOf(Line(A,C)))]."
Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent.,"[Find(x)] to nearest tenth. [Tangent(Line($),Circle($))]."
Find BC.,"[Find(LengthOf(Line(B,C)))]."
Find x. Round to the nearest tenth.,[Find(x)]. Round to nearest tenth.
"For the pair of similar figures, use the given areas to find x.","[Similar(Shape($1),Shape($2))], to [Find(x)]."
"In the figure, m \angle 1 = 50 and m \angle 3 = 60. Find the measure of \angle 8.",", [Equals(MeasureOf(Angle(1)),50)] and [Equals(MeasureOf(Angle(3)),60)] [Find(MeasureOf(Angle(8)))]."
"m \angle BAC = 38, BC = 5, and DC = 5, find m \angle DAC.","[Equals(MeasureOf(Angle(B,A,C)),38)] [Equals(LengthOf(Line(B,C)),5)] and [Equals(LengthOf(Line(D,C)),5)] [Find(MeasureOf(Angle(D,A,C)))]."
Find the measure of m \angle 2. Assume that segments that appear tangent are tangent.,"[Find(MeasureOf(Angle(2)))]. [Tangent(Line($),Circle($))]."
"In \odot O, EC and AB are diameters, and \angle BOD \cong \angle DOE \cong \angle EOF \cong \angle FOA. Find m \widehat AC.","[Circle(O)], [IsDiameterOf(Line(E,C),Circle(O))], [IsDiameterOf(Line(A,B),Circle(O))] and [Equals(Angle(B,O,D),Angle(D,O,E))], [Equals(Angle(D,O,E),Angle(E,O,F))], [Equals(Angle(E,O,F),Angle(F,O,A))]. [Find(MeasureOf(Arc(A,C)))]."
Find x. Assume that segments that appear to be tangent are tangent. Round to the nearest tenth if necessary.,"[Find(x)]. [Tangent(Line($),Circle($))]. Round to nearest tenth if necessary."
\triangle BCD \cong \triangle WXY. Find x.,"[Congruent(Triangle(B,C,D),Triangle(W,X,Y))]. [Find(x)]."
Use parallelogram PQRS to find QP.,"Use [Parallelogram(P,Q,R,S)] to [Find(LengthOf(Line(Q,P)))]."