A circle centered at point O is described around an isosceles triangle ABC, in which AB = BC

A circle centered at point O is described around an isosceles triangle ABC, in which AB = BC and an angle ABC = 49 degrees. Find the BOC angle.

The triangle ABC, AO condition is isosceles, then the angle BAC = BCA = (180 – ABC) / 2 = (180 – 49) / 2 = 131/2 = 65.5.

The inscribed angle BAC rests on the BC arc, then the degree measure of the BC arc is equal to the degree measure of the BAC angle. Arc BC = 65.5.

The central angle of the ВOC is also based on the arc of the BC, then the angle of the ВOC is equal to two degree measures of the arc of the BC.

Angle BOС = 2 * BC = 2 * 65.5 = 131.

Answer: The ВOC angle is 131.