In triangle ABC, angle A is three times greater than angle B and is equal to half of angle C.

In triangle ABC, angle A is three times greater than angle B and is equal to half of angle C. What is the sum of angles A and B?

1. We take the degree measure ∠B for x, ∠ A = 3x, ∠ C = 6x.

2. Considering that the total value of all internal angles of the triangle is 180 °, we will compose the equation:

3x + 6x + x = 180 °;

10x = 180 °;

x = 18 °;

∠В = 18 °.

∠A = 18 x 3 = 54 °.

∠С = 18 x 6 = 108 °

3. We calculate the total value of ∠А and ∠В:

∠А + ∠В = 54 + 18 = 72 °.

Answer: the total value of ∠А and ∠В is equal to 72 °.