Find the angles of an isosceles triangle if you know that the angle at the base is 1/6 of the angle between the sides.

1. Let’s denote the degree measure of the angle at the base through x.

2. Determine the degree measure of the angle between the lateral sides:

6 * x = 6x.

3. Since the sum of the angles of the triangle is 180˚, compose and solve the equation:

6x + x + x = 180˚;

8x = 180˚;

x = 180˚: 8;

x = 22.5˚.

4. The degree measure of the angle at the base is x = 22.5˚.

5. What is the degree measure of the angle between the sides?

6 * x = 6 * 22.5˚ = 135˚.

Answer: the angles of an isosceles triangle are 22.5˚, 135˚, 22.5˚.