Find the angles of an equilateral triangle if the angle at the base is 2 times the angle opposite the base

An isosceles triangle is a triangle in which the sides are equal and the angles at the base are equal:

∠А = ∠С.

The sum of all the angles of the pipe holder, regardless of its type, is equal to 180º:

∠А + ∠В + ∠С = 180º.

Thus, if the angles at the base are twice as large as the angle opposite the base, then we express:

x – angle ∠В, opposite to the base;

2x – angles at the base ∠А and ∠С;

x + 2x + 2x = 180;

5x = 180;

x = 180/5 = 36;

∠В = 36º;

∠А = ∠С = 2 · 36 = 72º.

Answer: angles ∠А and ∠С are equal to 72º, angle ∠В is equal to 36º.