Question

Point C is the center of the circle. What is the measure of angle ACB if arc ADB measures 250 degrees?

Answer 1

Around the outside of a circle measures 360°. If arc ADB measures 250°, then arc AB measures 360-250 which is 110°. Because point C is the center of the circle, then angle ACB is a central angle. By definition of an arc intercepted by an angle, they are the exact same measure in degrees. So if arc AB = 110, then the measure of the angle ACB also measures 110.