Find Angle OSQ Angle SOR

Step 1: Find Angle OSQ.
In the circle, $OQ$ and $OS$ are radii. Therefore, $OQ = OS$.
This means that $\triangle OQS$ is an isosceles triangle.
In an isosceles triangle, the angles opposite the equal sides are equal: $\angle OQS = \angle OSQ$.
The sum of angles in a triangle is $180^\circ$.
We are given $\angle QOS = 108^\circ$.

$$\angle QOS + \angle OQS + \angle OSQ = 180^\circ$$ $$108^\circ + \angle OSQ + \angle OSQ = 180^\circ$$ $$$$