A circle centered at point O is described about an isosceles triangle ABC, in which AB = BC and ∠ABC = 177 °. Find the angle BOC.

1) the sum of the angles of the triangles = 180 degrees. Hence the angle a = angle c = (180-177) / 2 = 1.5.
2) the angle в is inscribed, equal to the half of the arc on which it rests. 177 * 2 = 354 degrees. – arc ac.
3) the whole circle = 360 degrees. Hence the arc av + arcavs = 360-354 = 6 degrees.
4) arc ab = angle c * 2 = 1.5 * 2 = 3 degrees.
5) the arc means sun = 6-3 = 3 degrees.
6) the angle vos is central, equal to the arc on which it rests. Angle vos = 3 deg.
Answer: 3