The angles of a triangle are 1: 2: 9. Find the smaller corner of the triangle.

From the condition it is known that the angles of the triangle are related as 1: 2: 9. In order to find the smaller angle of the triangle, we compose and solve a linear equation.

First of all, we introduce the coefficient of similarity x and write the angles of the triangle as x; 2x and 9x.

You also need to know the sum of the angles of the triangle. The angles of a triangle add up to 180 °.

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

x + 2x + 9x = 180;

12x = 180;

x = 180: 12;

x = 15.

The coefficient of similarity is found. Now find the smaller angle 1 * x = 1 * 15 = 15 °.