Find the angles of triangle ABC if the angle is A: B: C = 1: 3: 5.

From the condition it is known that the angle of the triangle ABC, are related as A: B: C = 1: 3: 5.

In order to find the angles of the triangle, we introduce the coefficient of similarity x and write the angle of the triangle as x; 3x and 5x.

We also need a theorem on the sum of the angles of a triangle. It says that the sum of the angles of the triangle is 180 °.

Let’s compose and solve a linear equation with one variable.

x + 3x + 5x = 180;

9x = 180;

x = 180: 9;

x = 20.

Now let’s write down the degree measure of each angle:

1 * 20 = 20 °;

3 * 20 = 60 °;

5 * 20 = 100 °.

Answer: 20 °; 60 °; 100 °.