Question

Please help!! Having a hard time with this question...!

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…


(Please answer the question presented in the format in the question)

Answer 1

Explanation:

The angle you can get right away is z.

z + 93 = 180

z + 93 - 93 = 180 - 93

z = 87

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The next step is to solve for y. You need to draw a line from y to the center and another one from z to the center.

The triangle containing part of y and part of z has a central angle of 106 degrees.

Part of y + partz + 106 = 180

part of y + partz = 74

part of y = partz = 37 The triangle is isosceles because 2 of the legs are radii.

Do the same thing from 93 to the center and the other part of y to the center.

The central angle is 58

The two other angles are equal

part of y + part of 93 + 58 = 180

partofy + partof93 = 180 - 58

partofy + partof93 = 122

partofy = part93 = 61

So

y = 61 + 37 = 98

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x + y = 180 (opposite angles in a quadrillateral that fits in a circle = 180)

x + 98 = 180

x = 82

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x = 82

y = 98

z = 87