In triangle ABC, angle B = 70, angle C = 60, point O is the center of the circumscribed circle.

In triangle ABC, angle B = 70, angle C = 60, point O is the center of the circumscribed circle. Find the value of the angle BOC

Let us find the unknown angle A of the triangle ABC, if the other two angles are known by the condition:
Angle A = 180 ° – (angle B + angle C) = 180 ° – (70 ° + 60 °) = 180 ° – 130 ° = 50 °.
Angle A is not only the angle of the triangle ABC, it is also the inscribed angle BAC. It rests on the same arc on which the central angle of the BOС rests, which we need to find. By the inscribed angle theorem, we can write:
angle BAC = 1/2 * angle BOC, it follows from this:
BOC angle = 2 * BAC angle = 2 * 50 ° = 100 °.
Answer: the angle BОС is equal to 100 °.