Find the angles of the triangle ABC, where AB = BC if the angle at the base is 2 times less than the outer angle adjacent to it.

1. Let’s denote the angle at the base of the triangle ABC through x.

2. Determine the value of the angle adjacent to the angle at the base:

2 * x = 2x.

3. Let’s compose and solve the equation:

2x + x = 180˚;

3x = 180˚;

x = 180˚: 3;

x = 60˚.

4. The angle at the base of the triangle ABC is x = 60˚.

5. What is the angle at the apex of the triangle ABC?

180˚ – 2 * 60˚ = 180˚ – 120˚ = 60˚.

Answer: the angles of the triangle ABC are equal to 60˚, 60˚, 60˚.