# In triangle ABC, ∠A – ∠B = 15° and ∠B – ∠C = 30°, find ∠A, ∠B, and ∠C.

In a triangle ABC, it is given that

A – B = 15° and B – C = 30°

⇒ ∠A = B + 15° and C = B – 30°

We know that the sum of the angles of a triangle is 180°.

⇒ ∠A + B + C = 180°

⇒ ∠B + 15° + B + B – 30° = 180°

3B = 180° + 15°

3B = 195°

⇒ ∠B = 65°

So, A = B + 15° =65°+15° = 80°

C = B – 30°= 65°- 30° = 35°

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