In $Δ A B C$ , $∠ A - ∠ B = 16$ and $∠ C - ∠ A = 34$ ; find all the angles of the triangle.

∠ A = 32, ∠ B = 38 a n d ∠ C = 88

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∠ A = 54, ∠ B = 38 a n d ∠ C = 88

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∠ A = 44, ∠ B = 38 a n d ∠ C = 88

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∠ A = 62, ∠ B = 38 a n d ∠ C = 88

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Solution

The correct option is B $∠ A = 54, ∠ B = 38 a n d ∠ C = 88$
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, $∠ A = 54$
$∠ B = 38$

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