Question

Quadrilateral ABCD ​ is inscribed in a circle.

What is the measure of angle A?



Enter your answer in the box.

m∠A= ____°

Answer 1

2(4x+5)+2(x+15)=360
8x+10+2x+30=360
10x=320
x=32

∠A=4×32+5=133º

Answer 2

133

Explanation:

Given is a cyclic quadrilateral ABCD.

We know that in a cyclic quadrilateral, opposite angles are supplementary.

A+C =180

Given that A = 4x+5 and C = x+15

Add these and equate to 180

`4x+5+x+15 =1805x=180-20 =160x=32A= 4(32)+5 =133`

Verify:

When x= 32, Angle C = 47

A+C = 133+47 = 180

Hence right answer