Question

A circle has center O, and points R and S lie on the circle. In triangle ORS, the measure of ZROS is 88°. What is the measure of ZRSO, in degrees?​

Answer 1

Since O is the center of a circle, and RS is a chord, then angle ROS is an inscribed angle and angle RSO is a central angle. Therefore the measure of RSO is twice the measure of ROS, or 88*2 = 176. Since the angles in a triangle sum to 180, then the measure of ZRSO is 180-176-88 = 16. So the answer is 16