In triangle ABC, AB = AC, AH-bisector, angle ABC = 57 ‘. Find the angles of triangle ABC.

In a triangle ABC, the sides AB = AC, which means this triangle is isosceles. In an isosceles triangle, the angles at equal sides are also equal. Thus, the angles ABC and ACB are equal to each other and their degree measure is 57 °.

It is known that the sum of all the angles of a triangle is 180 °. Since the magnitude of the two angles is known, the third angle can be expressed as:

angle BAC = 180 – (angle ABC + angle ACB) = 180 – (57 + 57) = 76 °.

Answer: in triangle ABC angles ABC = ACB = 57 °, BAC = 76 °.