A quadrilateral is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work and/or explain how you got your answer. m∠z= I know this be…

Question

asked Feb 17, 2020 222k views

1 Answer

Naugtur · Answer 1 · 2020-02-24T07:01:24+0000

Answer:

Part 1) The measure of angle Z is
$87\°$

Part 2) The measure of angle x is
$82\°$

Part 3) The measure of angle y is
$98\°$

Explanation:

we know that

In a inscribed quadrilateral opposite angles are supplementary

so

In this problem

$93\°+z=180\°$ ------> equation A

$x+y=180\°$ ----> equation B

step 1

Find the measure of angle Z

Solve the equation A

$93\°+z=180\°$

solve for z

$z=180\°-93\°=87\°$

step 2

Find the measure of angle x

we know that

The inscribed angle is half that of the arc it comprises.

so

$m<x=(1)/(2)(58\°+106\°)= 82\°$

step 3

Find the measure of angle y

Solve the equation B

$x+y=180\°$

we have

$x=82\°$

substitute

$82\°+y=180\°$

$y=180\°-82\°=98\°$