Question

Quadrilateral ABCD ​ is inscribed in a circle. What is the measure of angle A?

Answer 1

Answer:

The measure of angle A = 133°

Step-by-step explanation:

The sum of opposite angles of cyclic quadrilateral is 180°

From the figure we can see that,quadrilateral ABCD ​ is inscribed in a circle.

<A + <C = 180°

To find the value of x

we have,

(4x + 5) + (x + 15) = 180

4x + 5 + x + 15 = 180

5x + 20 = 180

5x = 180 - 20 = 160

x = 160/5 = 32

To find the measure of angle

m<A = 4x + 5

x = 32

m<A = 4*32 + 5 = 128 + 5 = 133°

Therefore the measure of angle A = 133°