College

Find x, y, and z. If necessary, round to the tenths place. A. x = 23, y = 44.5, z = 116 B. x = 23, y = 89, z = 116 C. x = 44.5, y = 44.5, z = 116 D. x = 66, y = 89, z = 116

Find x y and z If necessary round to the tenths place A x 23 y 44 5 z 116 B x 23 y 89

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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