The angle at the base of an isosceles triangle is 2 times the angle between the lateral sides.

The angle at the base of an isosceles triangle is 2 times the angle between the lateral sides. Then the angle at the apex of an isosceles triangle will be equal to.

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

In the initial data for this task, it is reported that this triangle is isosceles, therefore, the angles at the base of this triangle are equal and the value of the second angle at the base of this triangle should also be equal to α.

According to the condition of the problem, the angle at the base of an isosceles triangle is 2 times the angle between the lateral sides, therefore, the value of the angle lying against the base should be equal to α / 2.

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

α + α + α / 2 = 180,

solving which, we get:

5α / 2 = 180;

α / 2 = 180/5;

α / 2 = 36.

Therefore, the angle at the apex of this triangle is 36 °.

Answer: 36 °.