The bisector AK is drawn in the isosceles triangle ABC with the base of the AC. Find the angle B

The bisector AK is drawn in the isosceles triangle ABC with the base of the AC. Find the angle B if the angle AKC = 87 degrees.

Since AC is the base of the isosceles triangle ABC, the angles A and C are equal (we denote them as x). Since AK is a bisector, the angles BAK and KAC are equal (that is, BAK = KAC = A / 2). Then, in the triangle AKC, the angle KAC is x / 2, the angle AKС is 87 degrees, and the angle C = x. Find the value of x using the triangle sum theorem:
KAC angle + AKC angle + C angle = 180 degrees;
x / 2 + 87 + x = 180;
3x / 2 = 93;
3x = 186;
x = 186/3;
x = 62 degrees.
In triangle ABC, angle A = angle C = 62 degrees. Find angle B:
angle A + angle B + angle C = 180 degrees;
62 + angle B + 62 = 180;
angle B = 180 – 124;
angle B = 56 degrees.
Answer: angle B = 56 degrees.