Question

In cyclic quadriletral abcd angleb-d=60 ,then find smaller of the angle b and d

Answer 1

ABCD ia a cyclic quadrilateral ,therefore:-

A+C=180°………..(1) & B+D=180°……………(2)

A-C=60°…………….(3)…..GIVEN.

On adding eq.(1) and (3)

2A=240° => A=120°

Put A=120° in eq.(1)

120°+C=180°

C=180–120=60°

It shows C<A , and C=60° . Proved.

Answer 2

In a cyclic quadrilateral, opp. angles are supplementary.
I. e. /_ b + /_d = 180...........1
Given that /_b - /_d= 60............2

adding (1) and (2)
/_b+/_d +/_b - /_d= 180+60
2/_b= 240
/_b= 120.

smaller angle /_ d= 180-120
= 60.