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4 years ago

Quadrilateral ABCD is inscribed in this circle.

Mathematics

1 answer:

Dafna11 [192]4 years ago

8 0

Answer:
measure angle C = 92 degrees

Explanation:
Quadrilateral ABCD is known as a cyclic quadrilateral. This means that it has all its vertices on the circle's circumference.
In a cyclic quadrilateral, the sum of each two opposite angles is 180 (check the attached image).
Therefore:
measure angle B + measure angle D = 180
x + 10 + x + 24 = 180
2x + 34 = 180
2x = 180 - 34
2x = 146
x = 73

We are given that:
measure angle A = x + 15
Therefore:
measure angle A = 73 + 15 = 88 degrees

Finally, we have:
measure angle A + measure angle C = 180
88 + measure angle C = 180
measure angle C = 180 - 88
measure angle C = 92 degrees

Hope this helps :)

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Quadrilateral ABCD ​ is inscribed in this circle.

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