In an isosceles triangle, the bisectors of the angles at the base form an angle of 52

In an isosceles triangle, the bisectors of the angles at the base form an angle of 52 degrees at the intersection. Find the angle at the apex of this triangle.

Given:
ABC – isosceles triangle
ВA = BC
AN = CM – bisectors
T.О – intersection point of bisectors
angle MOA = 52
Find: angle B-?
Decision:
angle AOC = 180 – angle MOA = 180-52 = 128;
triangle AOС is equal to femoral (AO = OС);
angle OAC + angle OCA = 180-angle AOC = 180-128 = 52;
angle ОАС = angle ОАС = 52: 2 = 26;
angle BAC = angle BAO + angle OAC = 26 + 26 = 52 (as the AO bisector).
In triangle ABC:
angle A = angle C = 52;
angle C = 180-angle A – angle C = 180-52-52 = 76.
Answer: angle B = 76.