Answer:
92
Step-by-step 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
