Question

​ Quadrilateral ABCD ​ is inscribed in this circle. What is the measure of angle C? Enter your answer in the box.

Answer 1

62 i took the test

Explanation:

Answer 2

`m<C=62\°`

Explanation:

we know that

In an inscribed quadrilateral opposite angles are supplementary

so

In this problem

`m<D+m<B=180\°`

`m<C+m<A=180\°`

step 1

Find the value of x

`m<D+m<B=180\°`

substitute the values and solve for x

`(x+20)\°+(3x)\°=180\°`

`4x=180\°-20\°`

`x=160\°/4=40\°`

step 2

Find the measure of angle A

`m<A=(2x+38)\°=2(40\°)+38\°=118\°`

step 3

Find the measure of angle C

`m<C+m<A=180\°`

substitute the values and solve for m<C

`m<C+118\°=180\°`

`m<C=180\°-118\°=62\°`