Question

Quadrilateral ABCD is inscribed in a circle. What is the measure of angle C? Show your work. Thanks.

Answer 1

quadilateral inside circle follow these rules

sum of opposite angles is 180

so

B + D = 180

C + A = 180

x + 24+ x + 10 = 180

2x + 34 = 180

2x = 180-34 = 146

x = 146/2 = 73

A + C = 180

x + 15 + c = 180

73 + 15 + C = 180

88 + C = 180

C = 180- 88 = 92

C = 92

Answer 2

92

Explanation:

Remark

This kind of quadrilateral (one inscribed in a circle) is called a cyclic quadrilateral.

It has the unusual properties of opposite angles being supplementary. That means they add to 180o

Givens

B + D = 180 degrees

C + A = 180 degrees

Solution

Work with <B + <D = 180o

x + 24 + x + 10 = 180 Collect like terms on the left.

2x + 34 = 180 Subtract 34 for both sides

2x +34-34 = 180-34 Combine

2x = 146 Divide by 2

x = 146/2

x = 73

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Now work with A + C = 180

A = x + 15

A = 73 + 15

A = 88

88 + C = 180 Subtract 88 from both sides.

88 - 88 + C = 180 - 88

C = 92