joshdunsbuns143
contestada

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 because…

m∠x=

I know this because…

m∠y=

I know this because…

A quadrilateral is inscribed in a circle Find the measure of each of the angles of the quadrilateral Show your work andor explain how you got your answer mz I k class=

Respuesta :

calculista

Answer:

Part 1) The measure of angle Z is [tex]87\°[/tex]

Part 2) The measure of angle x is [tex]82\°[/tex]

Part 3) The measure of angle y is [tex]98\°[/tex]

Step-by-step explanation:

we know that

In a inscribed quadrilateral opposite angles are supplementary

so

In this problem

[tex]93\°+z=180\°[/tex] ------> equation A

[tex]x+y=180\°[/tex]----> equation B

step 1

Find the measure of angle Z

Solve the equation A

[tex]93\°+z=180\°[/tex]

solve for z

[tex]z=180\°-93\°=87\°[/tex]

step 2

Find the measure of angle x

we know that

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

so

[tex]m<x=\frac{1}{2}(58\°+106\°)= 82\°[/tex]

step 3

Find the measure of angle y

Solve the equation B

[tex]x+y=180\°[/tex]

we have

[tex]x=82\°[/tex]

substitute

[tex]82\°+y=180\°[/tex]

[tex]y=180\°-82\°=98\°[/tex]