$I n Δ A B C, i f ∠ A + ∠ B = 108^{\circ} a n d ∠ B + ∠ C = 130^{\circ}, f i n d ∠ A, ∠ B a n d ∠ C .$

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Solution

$L e t ∠ A + ∠ B = 108^{\circ} a n d ∠ B + ∠ C = 130^{\circ} . \Rightarrow ∠ A + ∠ B + ∠ B + ∠ C = 108^{\circ} + 130^{\circ} \Rightarrow ∠ A + ∠ B + ∠ C + ∠ B = 238^{\circ} ∵ ∠ A + ∠ B + ∠ C = 180^{\circ} \Rightarrow 180^{\circ} + ∠ B = 238^{\circ} \Rightarrow ∠ B = 58^{\circ} ∴ ∠ C = 130^{\circ} - ∠ B = 130^{\circ} - 58^{\circ} = 72^{\circ} ∴ ∠ A = 108^{\circ} - ∠ B = 108^{\circ} - 58^{\circ} = 50^{\circ}$

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In $Δ A B C$ , if $∠ A + ∠ B = 125^{\circ}$ and $∠ A + ∠ C = 113^{\circ}$ , find $∠ A, ∠ B$ and $∠ C$ .

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