Question

Quadrilateral ABCD is inscribed in this circle. What is the measure of angle A? Show your work.

Answer 1

quadilateral inside circle follow these rules

sum of opposite angles is 180

so

B + D = 180

C + A = 180

x + 116 = 180

x = 180-116 = 64


A = 2×64 -40 = 128 -40
A = 88

Answer 2

88°

Explanation:

Angles B and D are supplementary, so the value of x is ...

x = 180° -116° = 64°

Then the measure of angle A is ...

(2x -40)° = (2·64 -40)° = 88°

The measure of angle A is 88°.