Question

​ Quadrilateral ABCD ​ is inscribed in this circle.

What is the measure of angle C?

Answer 1

The measure of angle C = 92°

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.

To find the value of x

m<B + m<D = 180°

(x + 10 ) + ( x + 24 ) = 180

x + 10 + x + 24 = 180

2x + 34 = 180

2x = 180 - 34 = 146

x = 146/2 = 73

To find the measure of <A

m<A = x + 15

x = 73

m<A = 73 + 15 = 88°

To find the measure of <C

m<C + m<A = 180°

m<C + 88 = 180

m<C = 180 - 88 = 92°

Therefore the measure of angle C = 92°