In triangle ABC, angle A is 3 times greater than angle B, and angle C is 20 times less. Find the angles of the triangle.

By the theorem on the sum of the angles of a triangle: The sum of the angles of a triangle is 180 °.

Let the angle B of the triangle ABC be equal to x degrees, then the angle A is 3x degrees (if it is 3 times larger, then it must be multiplied by 3), and the angle C is (x – 20) (if it is less by 20, then it is necessary to subtract 20) … The sum of the angles of the triangle ABC is (3x + x + (x – 20)) degrees or 180 degrees. Let’s make an equation and solve it.

3x + x + (x – 20) = 180;

3x + x + x – 20 = 180;

5x – 20 = 180;

5x = 180 + 20;

5x = 200;

x = 200: 5;

x = 40 ° – angle B;

3x = 40 * 3 = 120 ° – angle A;

x – 20 = 40 – 20 = 20 ° – angle C.

Answer. 120 °; 40 °; 20 °.