∠A, ∠B, ∠C are three angles of a triangle. If

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∠A, ∠B, ∠C are three angles of a triangle. If ∠A – ∠B = 15°, ∠B – ∠C = 30°, then ∠A, ∠B and ∠C are

1. 80°, 60°, 40°
2. 70°, 50°, 60°
3. 80°, 65°, 35°
4. 80°, 55°, 45°

Correct Option: C

Here , ∠B – ∠C = 30°, ∠A – ∠B = 15°
∴ ∠A + ∠B + ∠C = 180° ....(i)
(∠B – ∠C) – (∠A – ∠B) = 30° – 15°
⇒ 2 ∠B – ∠A – ∠C = 15° ....(ii)
By adding (i) and (ii), we get
3∠B = 180° + 15° = 195°
⇒ ∠B = 65°
∠A – ∠B = 15°
⇒ ∠A = 15° + 65° = 80°
And ∠B – ∠C = 30°
⇒ ∠C = ∠B – 30° = 65° – 30° = 35°