Answer :
The measure of angle x is 23⁰.
The value of arc angle y is 45.5⁰.
The value of arc angle z is 116⁰.
What is the value of x, y and z?
The measure of angle x, y and z is calculated as follows;
∠mEGF = ¹/₂ (arc EF - arc DC ) (intersecting chord theorem)
33 = ¹/₂ (89 - x )
2(33) = 89 - x
66 = 89 - x
x = 89 - 66
x = 23⁰
The value of arc angle z is calculated as follows;
89 + 132 + 23 + z = 360 (sum of angles of a circle)
244 + z = 360
z = 360 - 244
z = 116⁰
The value of angle y is calculated as follows;
∠mGEF = ¹/₂(z) (intersecting chord theorem)
∠mGEF = ¹/₂(116)
∠mGEF = 58⁰
∠mEFG = 180 - (58 + 33) = 89
y + 89 + y = 180 (sum of angles on a straight line)
2y + 89 = 180
2y = 91
y = 91/2
y = 45.5⁰
Learn more about chord angles here: brainly.com/question/23732231
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