Find the angle at the base of an isosceles triangle if you know that one of its angles is 2 times smaller than the other angle.

There are two possible cases in this problem. The first is when the apex angle is greater than the base angle and vice versa, the apex angle is less than the base angle. Let’s consider each case.
1. Enter the variable x and denote the angle at the base this way, the second angle at the base is also x, and the angle at the top 2x. Let’s make the equation:
x + x + 2x = 180 °
4x = 180 °
x = 45 ° – angle at the base;
45 ° * 2 = 90 ° – apex angle.
2. We denote by variable x the angle at the top, and the angle at the base will be 2x. We get the equation:
x + 2x + 2x = 180 °
5x = 180 °
36 ° – apex angle;
36 ° * 2 = 72 ° – angle at the base.