In triangle ABC, angle B is 2 times greater than angle A, and angle C is 20 degrees greater

In triangle ABC, angle B is 2 times greater than angle A, and angle C is 20 degrees greater than angle A. Find the angles of triangle ABC.

Given:

ABC – triangle,

angle B = 2 * angle A,

angle C = angle A + 20.

Find the degree measures of the angles of the triangle ABC: angle A, angle B, angle C

Solution:

Consider a triangle ABC.

Let the degree measure of angle A be equal to x degrees, then the degree measure of angle B is equal to 2 * x degrees, and angle C is equal to (x + 20) degrees. We know that the sum of the degree measures of a triangle is 180 degrees. Let’s make the equation:

x + 2 * x + x + 20 = 180;

x + 2 * x + x = 180 – 20;

x + 2 * x + x = 160;

x * (1 + 2 + 1) = 160;

x * 4 = 160;

x = 160: 4;

x = 40 ° – the degree measure of the angle A;

2 * 40 = 80 ° – degree measure of angle B;

40 + 20 = 60 ° is the degree measure of the angle C.

Answer: 40 °; 80 °; 60 °.