Find the angles of an isosceles triangle if the angle opposite the base is 24 degrees less than the angle m at the base.

An isosceles triangle is a triangle in which the sides are equal.

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

∠А = ∠С.

Since the angle opposite to the base (∠B) is 24º less than the angle at the base, and the sum of all the angles of the triangle is 180º, then we express:

x is the degree measure of the angle ∠В;

x + 24 – degree measure of angles ∠А and ∠С;

x + x + 24 + x + 24 = 180;

x + x + x = 180 – 24 – 24;

3x = 132;

x = 132/3 = 44;

∠В = 44º;

∠А = ∠С = 44 + 24 = 68º.

Answer: the degree measure of the angle opposite to the base is 44 degrees, the degree measure of the angles at the base is 68 degrees.