In ΔABC,∠A−∠B=16∘ and ∠C−∠A=34∘; find the angles of the triangle.
A
∠A=44∘,∠B=38∘ and ∠C=88∘
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B
∠A=54∘,∠B=38∘ and ∠C=88∘
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C
∠A=32∘,∠B=38∘ and ∠C=88∘
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D
∠A=60∘,∠B=38∘ and ∠C=88∘
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Solution
The correct option is B∠A=54∘,∠B=38∘ and ∠C=88∘ Given, ∠A−∠B=16..(I) ∠C−∠A=34...(II) Also, sum of angles of the triangle, ∠A+∠B+∠C=180...(III) Add all the equations, ∠A+2∠C=180+16+34 ∠A+2∠C=230 (IV) Add II and IV 3∠C=230+34 ∠C=88 From I and II, ∠A=54 ∠B=38