OG详解-OG4 数学1 Q20

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°. It follows that points R and S lie on the circle. Therefore, OR​ and 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, ∠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, ∠ROS is 100.