Question

Quadrilateral abcd is inscribed in a circle. M angle C is 64 degrees, M angle B is (6x+4) degrees, M angle C is (9x-1) degrees. What is the measure of angle D?

Answer 1

We are given that angle C is (9x - 1) degrees, and that this is equal to 64 degrees. Therefore,
9x - 1 = 64
9x = 65
x = 65/9
This means that angle B is (6x + 4) = 6(65/9) + 4 = 47 and 1/3 degrees.
In a cyclic quadrilateral, opposite angles add up to 180 degrees, so angle D + angle B = 180
angle D = 180 - angle B
angle D = 180 - (47 1/3)
angle D = 132 2/3 degrees