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?

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