Find the angles of an isosceles triangle if the apex angle is 3 times the base angle.

In order to find the angles of an isosceles triangle, if the angle at the apex is 3 times the angle at the base, we compose and solve a linear equation with one variable.

We denote by the variable x the angle at the base of an isosceles triangle, then the angle at the apex is 3x.

From the property of the angles of an isosceles triangle, we know that the angles at the base of an isosceles triangle are equal. And the sum of the angles of a triangle is 180 °.

x + x + 3x = 180;

5x = 180;

x = 36 ° angles at the base;

3 * 36 = 108 ° apex angle.