what is the measure of ∠c? 38° 76° 90° 152°

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Identify the intercepted arc

The inscribed angle $\angle C$ intercepts arc $AB$. The measure of arc $AB$ is given as $76^{\circ}$.

Step3: Calculate the measure of $\angle C$

By the inscribed - angle theorem, $m\angle C=\frac{1}{2}m\overset{\frown}{AB}$. So $m\angle C = \frac{76^{\circ}}{2}=38^{\circ}$.

Answer:

$38^{\circ}$