Find the angles of an isosceles triangle if the angle at the base is 36 degrees greater than at the apex

In an isosceles triangle, the angles at the base are:

∠А = ∠С.

Since the sum of the degree measures of all angles of the triangle is 180 degrees, and the degree measure of the angles ∠A and ∠C at the base is 36º greater than the value of the angle ∠B at the apex, we express it as follows:

x – degree measure of angle ∠В;

x + 36 – the degree measure of the angles ∠А and ∠С;

x + x + 36 + x + 36 = 180;

x + x + x = 180 – 36 – 36;

3x = 108;

x = 108/3 = 36;

∠В = 36º;

∠А = ∠С = 36º + 36º = 72º.

Answer: The degree measure of the angles at the base is 72º, the angle at the apex is 36º.