Circles SAT question

The correct answer is $100$. It's given that point $O$ is the center of a circle and the measure of arc $RS$ on the circle is $100^{\circ }$. It follows that points $R$ and $S$ lie on the circle. Therefore, $\overline{\mathrm{OR}}$ and $\overline{\mathrm{OS}}$ are radii of the circle. A central angle is an angle formed by two radii of a circle, with its vertex at the center of the circle. Therefore, $\angle ROS$ is a central angle. Because the degree measure of an arc is equal to the measure of its associated central angle, it follows that the measure, in degrees, of $\angle ROS$ is $100$.