Geometry - Solved Examples

Q 1 - A line has
A - One end point
B - Two end points
C - Three end points
D - No end points
Answer - D
Explanation
A line has no points.

Q 2 - A line segment has
A - One end point
B - Two end points
C - Three end points
D - No end points
Answer - B
Explanation
A line segment has two end points.

Q 3 - A ray has
A - One end point
B - Two end points
C - Three end points
D - No end points
Answer - A
Explanation
A ray has one end point.

Q 4 - An angle which is greater then 180° but less than 360° is called
A - Acute Angle
B - Obtuse Angle
C - Straight Angle
D - Reflex Angle
Answer - B
Explanation
An angle which is greater than 180°  but less than 360° is called a reflex angle.

Q 5 - The complement of 62°  is.
A - 118°
B - 28°
C - 38°
D - 48°
Answer - B
Explanation
Complement of 62°= (90° – 62°) = 28°.

Q 6 - The supplement of 60° is
A - 30°
B - 40°
C - 120°
D - 300°
Answer - B
Explanation
Supplement of 60° = (180°-60°) =120°.

Q 7 - The complement of 72° 40'  is 
A - 107°20' 
B - 27°20' 
C - 17°20' 
D - 12°40' 
Answer - C
Explanation
Complement of 72° 40' = (90°-72° 40') =17° 20'.

Q 8 - An angle is one fifth of its supplement. The measure of the angle is
A - 15°
B - 30°
C - 75°
D - 150°
Answer - B
Explanation
x = 1/5 (180 – x )⇒ 5x = 180 – x ⇒ 6x = 180 ⇒ x = 30°.

Q 9 - If an angle is its own complementary angle, then its measure is 
A - 30°
B - 45°
C - 60°
D - 90°
Answer - B
Explanation
x=(90-x) ⇒ 2x = 90 ⇒ x = 45° .

Q 10 - How many angles are made by rays shown in the figure?

A - 5
B - 6
C - 8
D - 10
Answer - D
Explanation
The angle are ∠AOB , ∠BOC,∠COD,∠DOE,∠AOC,∠AOD, ∠AOE,∠BOD,∠BOD,∠COE. 
Thus , 10 angle are  formed.

Q 11 - An angle is 24° more than  its complement.The measure of the angle is
A - 57°
B - 47°
C - 53°
D - 66°
Answer - A
Explanation
x – (90-x ) = 24 ⇒ 2x = 114 ⇒ x = 57
∴ Required angle is 57°.

Q 12 -An angle is 32° less than  its supplement. The measure of the angle is
A - 37°
B - 74°
C - 48°
D - 66°
Answer - A
Explanation
(180 –X) – X = 32 ⇒  2x = 180 – 32 = 148 ⇒ x = 74. 
Required angle is 74°.

Q 13 - Two Supplementary  angles are in th ratio 3:2. The smaller angle measures 
A - 108°
B - 81°
C - 72°
D - 66°
Answer - C
Explanation
Let the measures of the angle be (3x)° and (2x)°. Then, 
3x+2x=180 ⇒ 5x = 180 ⇒ x = 36.
Smaller angle = (2x)° = (2*36)° = 72°. 

Q 14 - In the given figure, AOB is a straight line, ∠AOC = 68° and	∠BOC = x°. The value of the x is 
A - 120°
B - 22°
C - 112°
D - 132°
Answer - A
Explanation
Since ∠AOB is a straight angle , we have
X+ 68 = 180 ⇒ x= (180-68)°  = 120°

Q 15 - In the given figure , AOB is a straight line,  ∠AOC = (3x+20)° and ∠ BOC =(4 x-36)°. The value of the x is 
A - 32°
B - 22°
C - 26°
D - 24°
Answer - B
Explanation
Since ∠AOB is a straight angle , we have 
∠AOC + ∠ BOC  =180° 
⇒ 3x + 20 +4x – 36 = 180
⇒ 7x = 164 ⇒ x = 22.

Q 16 - In the given figure , AOB is a straight line,  ∠ AOC = (3x-8)° and ∠COD =50 and ∠BOD° =(x+10)°. The value of the x is 
A - 32°
B - 42°
C - 36°
D - 52°
Answer - A
Explanation
Since ∠AOB is a straight angle , we have
∠AOC  + ∠ COB  + ∠ BOD  = 180° 
⇒ (3X – 8)° + 50° + (X+ 10)° = 180° 
⇒ 4X = 128 ⇒ X = 32. 


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