Find the angles of an isosceles triangle if the base angle is 48 degrees less than the apex angle.

In an isosceles triangle, the angles at the base are equal. Since the sum of all the angles of the triangle is 180º, and the angle at the base is 48º less than the angle at the apex, then:

x – angles at the base ∠А and ∠С;

x + 48 – angle at the vertex ∠В;

x + x + x + 48 = 180;

x + x + x = 180 – 48;

3x = 132;

x = 132/3 = 44;

∠А = ∠С = 44º;

∠В = 44º + 48º = 92º.

Answer: the angles at the base are 44º, the angle at the top is 92º.