In an isosceles triangle, the angle at the base is 2 times the angle at the apex opposite to the base

In an isosceles triangle, the angle at the base is 2 times the angle at the apex opposite to the base, find the angles of this triangle.

Let us denote by α the value of the angle at the apex of this isosceles triangle.

In the initial data for this task, it is reported that the angle at the base of this triangle is twice the value of the angle at its apex, therefore, the angle at the base should be equal to 2α.

Since this triangle is isosceles, the second angle at the base of this triangle should also be 2α.

Since in any triangle the sum of the angles is 180 °, we can make the following equation:

α + 2α + 2α = 180,

solving which, we get:

5α = 180;

α = 180/5 = 36 °.

Find the angle at the base:

2α = 2 * 36 = 72 °.

Answer: 36 °, 72 ° and 72 °.