Quadrilateral ABCD is inscribed in this circle.

What is the measure of angle C?

Enter your answer in the box.
°

Image shows a circle with inscribed quadrilateral A B C D. The measure of angle A is 2 x plus 3 degrees. The measure of angle B is 2 x minus 4 degrees. The measure of angle D is 3 x plus 9 degrees.

107

Step-by-step explanation:

First note that this quadrilateral is cyclic.

One property of cyclic quadrilaterals is that opposite angles add up to 180.

since B and D are opposite angles, we can add them and set that to 180. we get that 5x+5=180, so x=35. Now, substituting 37 for x for all the angles, we get

A=73

B=66

D=114

To find C, notice that A and C are opposite angles. This means they add up to 180

73+C=180, C=107

the sum of all the angles in a triangle are equal to 180

so you can add   the 3 given angles together to equal 180:

5y + 2y + 2y = 180

or since all three angles have the same letter, combine the 3 angles to equal 180:

9y = 180