In triangle ABC, the angle is 2 times the angle C, and the angle A is 54 degrees. determine the size of the angles B and C.

Let x be the angle C.

Since, in triangle ABC, angle B is 2 times greater than angle C, then angle B is equal to:

Angle B = 2 * angle C = 2 * x;

Angle A = 54 °.

Find the angles B and C.

The three angles of a triangle add up to 180 °.

Let’s make the equation:

x + 2 * x + 54 = 180;

x + 2 * x = 180 – 54;

3 * x = 180 – 50 – 4;

3 * x = 130 – 4;

3 * x = 126;

x = 126/3;

x = 120/3 + 6/3;

x = 40 + 2;

x = 42;

This means that the angle C of the triangle ABC is 42 °.

Find corner B.

Angle B = 2 * x = 2 * 42 ° = 2 * 40 ° + 2 * 2 ° = 80 ° + 4 ° = 84 °.

Answer: angle C = 42 ° and angle B = 84 °.