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 :)
