The angle at the apex of an isosceles triangle is 3 times the angle at the base.

The angle at the apex of an isosceles triangle is 3 times the angle at the base. Find the degree measures of the angles of the triangle.

By condition, an isosceles triangle ABC is given: AB = BC – sides, AC – base, ∠A = ∠C = x (since the angles at the base are equal), ∠B = 3 * ∠A = 3 * ∠C = 3 * x …

1. The theorem on the sum of the catch of a triangle states that the sum of all the internal catch of any triangle is 180 °. Thus:

∠A + ∠B + ∠C = 180 °;

x + 3 * x + x = 180 °;

5 * x = 180 °;

x = 180 ° / 5;

x = 36 °.

2. The angles of this triangle are equal:

∠A = ∠C = x = 36 °;

∠B = 3 * ∠A = 3 * ∠C = 3 * x = 3 * 36 ° = 108 °.

Answer: ∠A = 36 °, ∠B = 108 °, ∠C = 36 °.