Angle B of triangle ABC is half the angle A and 20 degrees more than angle C. Find the angles of triangle ABC.

Let the angle B be equal to x degrees. It is known. one hundred angle B is 2 times less than angle A, which means angle A, on the contrary, will be 2 times more than angle B and will be equal to 2x degrees. It is also known that the angle B is 20 degrees greater than the angle C, therefore the angle C, on the contrary, will be less by 20 degrees than the angle B and will be equal to (x – 20) degrees. We know that the sum of the angles of a triangle is 180 degrees, or (x + 2x + (x – 20)) degrees. Let’s make an equation and solve it.

x + 2x + (x – 20) = 180;

x + 2x + x – 20 = 180;

4x = 180 + 20;

4x = 200;

x = 200: 4;

x = 50 – angle B;

2x = 50 * 2 = 100 – angle A;

x – 20 = 50 – 20 = 30 – angle C.

Answer. 50, 100, 30.