Question 9

Explanation

Given $\angle BOC = 50^\circ$. Line $AOB$ is a straight line (diameter), so the straight angle is $180^\circ$.

Thus, we can find the measure of $\angle AOC$:

Consider triangle $\triangle AOC$. Since $O$ is the center of the circle, $OA$ and $OC$ are radii of the circle. Therefore, $OA = OC$, so triangle $\triangle AOC$ is an isosceles triangle.

In an isosceles triangle $\triangle AOC$, the base angles are equal, i.e., $\angle OAC = \angle OCA$.

The sum of angles in a triangle is $180^\circ$.

So, the measure of $\angle OAC$ is $25^\circ$.