# What is the measure of angle c?

May 16, 2018

$m \angle C = 102$

#### Explanation:

From the Inscribed Quadrilateral Theorem, we can state that:

$\angle D + \angle B = 180$

$2 x - 4 + 3 x + 9 = 180$

$5 x + 5 = 180$

$5 x = 175$

$x = 35$

We can also state that $\angle A + \angle C = 180$, or $2 x + 3 + m \angle C = 180$

We can solve for angle C by plugging in our x value, 35.

$2 \cdot 35 + 3 + m \angle C = 180$

$78 + m \angle C = 180$

$m \angle C = 102$