Can someone help me find this answer?

Question

asked Dec 28, 2020 166k views

1 Answer

Max Shron · Answer 1 · 2021-01-02T07:21:43+0000

Answer:

$m<D=106\°$

Explanation:

we know that

In a quadrilateral inscribed in a circle opposite angles are supplementary so

$m<A+m<C=180\°$

$m<B+m<D=180\°$

Step 1

Find the value of x

substitute the values

$x^(2) +3x=180\\ \\ x^(2) +3x-180=0$

using a graphing tool

solve the quadratic equation

see the attached figure

$x=12\°$

step 2

Find the measure of angle D

$m<B+m<D=180\°$

$m<B=7x-10=7(12)-10=74\°$

substitute

$74\°+m<D=180\°$

$m<D=180\°-74\°=106\°$