Question

Quadrilateral ABCD is inscribed in a circle. m angle A is 64°, m angle B is (6x + 4)°, and m angle C is (9x - 1)°. What is m angle D?

Answer 1

B and D are opposite angles, so they're supplementary.


m∠B + m∠D = 180° 82° + m∠D = 180° m∠D = 98°

Answer 2

`m<D=98\°`

Explanation:

we know that

The Inscribed Quadrilateral Theorem, states that a quadrilateral is inscribed in a circle if and only if the opposite angles are supplementary

so

In this problem

`m<A+m<C=180\°` -----> equation A

`m<B+m<D=180\°` -----> equation B

we have

`m<A=64\°`

`m<B=(6x+4)\°`

`m<C=(9x-1)\°`

Step 1

Find the value of x

substitute the measure of angle A and the measure of angle C in the equation A to find x

`64\°+(9x-1)\°=180\°`

`9x=180\°-64\°+1\°`

`9x=117\°`

`x=13\°`

Step 2

Find the measure of angle D

substitute the measure of angle B in the equation B to find m<D

`(6x+4)+m<D=180\°`

substitute the value of x

`(6(13)+4)+m<D=180\°`

`82\°+m<D=180\°`

`m<D=180\°-82\°=98\°`