In an isosceles triangle, the bisector drawn from the vertex of the angle at the base forms an angle of 60

In an isosceles triangle, the bisector drawn from the vertex of the angle at the base forms an angle of 60 with the side. Knowing that this angle is opposite to the base, find the angle at the base.

1. A, B, D – the vertices of the triangle. BH is the bisector. ∠ABH = 60 °.

2. By the condition of the problem, the triangle ABC is isosceles. Consequently, the bisector BH also performs the functions of height. That is, ∠АНB = 90 °.

3. Considering that the total value of all internal angles of the triangle is 180 °, we calculate the value of ∠АНB of the triangle АНB:

∠АНB (∠А) = 180 ° – ∠АНB – ∠АBН = 180 ° – 90 ° – 60 ° = 30 °.

Answer: The degree measure of the angle at the base of a given triangle (∠A) is 30 °.