Points A, B and C lie on a circle with center O, angle ABC = 50 degrees, AB: CB = 5: 8. Find the degree measure of the angle AOB.

Angle ABC – inscribed, it is equal to half of the arc on which it rests. That is, the AC arc is

50 * 2 = 100 °. The whole circle is 360 °.

Corner AOB is central. It is equal to the arc AB.

Arc AB + arc BC = 360 ° – arc AC = 360 ° – 100 ° = 260 °;

AB: CB = 5 8; Hence the arc AB = 260 °: (5 + 8) * 5 = 260 °: 13 * 5 = 100 °;

Therefore the angle AOB = 100 °.