TASK DEFINITION: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
PROBLEM: Problem: what is the measure of the angle w made by the diagonals of the any adjacent sides of a cube .
Options: a ) 30 , b ) 45 , c ) 60 , d ) 75 , e ) 90

SOLUTION: c

PROBLEM: Problem: a lady grows broccoli in her garden that is in the shape of a square . each broccoli takes 1 square foot of area in her garden . this year , she has increased her output by 79 broccoli when compared to last year . the shape of the area used for growing the broccoli has remained a square in both these years . how many broccoli did she produce this year ?
Options: ['a ) 1600', 'b ) 1500', 'c ) 1650', 'd ) 1700', 'e ) can not be determined']

SOLUTION: a

PROBLEM: Problem: in triangle pqr , the angle q = 90 degree , pq = 5 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz
Options: a ) 3.6 cm , b ) 2.4 cm , c ) 4.0 cm , d ) 2.16 cm , e ) 3.2 cm

SOLUTION:
c