Q10 of 34 Page 170

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°


⇒ 3∠B = 180° + 15°


⇒ 3∠B = 195°


⇒ ∠B = 65°


So, ∠A = ∠B + 15° =65°+15° = 80°


∠C = ∠B – 30°= 65°- 30° = 35°


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