Question #N205
In a circle with center O, points A, B, and C lie on the circle, and \overline{AC} is a diameter of the circle. If the measure of \angle AOB is 100 degrees, what is the measure of \angle ABC?
A. 25
B. 50
C. 60
D. 75
Correct Answer is: B
Since \overline{AC} is a diameter, \angle ACB is a right angle, and has a measure of 90 degrees. The measure of an inscribed angle is half the measure of its intercepted arc. The intercepted arc of \angle AOB is 100 degrees, so the measure of \angle ACB is 50 degrees. Therefore, the measure of \angle ABC is 180 degrees - 90 degrees - 50 degrees = 40 degrees.