Question

find the measure of angle c.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Let $\angle A = 117^{\circ}$, $\angle B=36^{\circ}$, and $\angle C$ be the unknown angle. So, $\angle A+\angle B+\angle C = 180^{\circ}$.

Step2: Solve for $\angle C$

We can rewrite the equation as $\angle C=180^{\circ}-\angle A - \angle B$. Substitute $\angle A = 117^{\circ}$ and $\angle B = 36^{\circ}$ into the equation: $\angle C=180^{\circ}-117^{\circ}-36^{\circ}$.
First, $180 - 117=63^{\circ}$, then $63^{\circ}-36^{\circ}=27^{\circ}$.

Answer:

$27^{\circ}$