In triangle ABC, angle B is 2.5 times angle A, and angle C is 24 degrees less than angle B. Find angle C

1. By the condition of the problem, ∠В = 2.5 times more than A. Therefore, ∠B = 2.5∠A.

2. By the condition of the problem, ∠C is 24 ° less than the angle ∠B. Hence, ∠C = ∠B – 24 ° = 2.5∠A – 24 °.

3. The total value of all angles of the triangle is 180 °:

∠A + ∠В ∠С = 180 °.

4. Substitute in this expression 2.5∠A instead of ∠B and (2.5∠A – 24 °) instead of ∠C:

∠A + 2.5∠A + 2.5∠A – 24 ° = 180 °.

6∠A = 204 °.

∠A = 34 °.

∠C = 2.5∠A – 24 ° = 2.5 x 34 – 24 = 85 – 24 = 61 °.