Question

In triangle ABC angle A - angle B =15 , angle B - angle C = 30, find angle B , angle A , angle C

Answer 1

∠A - ∠B = 15 → ∠A = 15 + ∠B

∠B = ∠B

∠B - ∠C = 30 → ∠C = ∠B - 30

Since ABC is a triangle, then their sum equals 180°

∠A + ∠B + ∠C = 180

(15 + ∠B) + (∠B) + (∠B - 30) = 180

3∠B - 15 = 180

3∠B = 195

∠B = 65

∠A = 15 + ∠B → ∠A = 15 + 65 → ∠A = 80

∠C = ∠B - 30 → ∠C = 65 - 30 → ∠C = 35

Answer: ∠A = 80, ∠B = 65, ∠C = 35