Find the angles of the triangle ABC if the angle A is 60 ° less than the angle B and 2 times less than the angle C.

Given:
triangle ABC,
angle B = angle A + 60 degrees,
angle C = 2 * angle A.
Find the degree measures of angle A, angle B, angle C -?
Decision:
Consider a triangle ABC. Let the degree measure of the angle A be equal to x degrees, the degree measure of the angle B = x + 60 degrees, the degree measure of the angle C is equal to 3 * x degrees. We know that the sum of the degree measures of any triangle is 180 degrees. Let’s make the equation:
x + x + 60 + 2 * x = 180;
x * (1 + 1 + 2) + 60 = 180;
x * 4 = 180 – 60;
x * 4 = 120;
x = 120: 4;
x = 30 degrees – the degree measure of the angle A;
30 + 10 = 40 degrees – the degree measure of the angle B;
2 * 30 = 60 degrees – the degree measure of the angle C.
Answer: 30 degrees; 40 degrees; 60 degrees.