In $△ A B C, ∠ A$ is $50^{o}$ . Find $∠ B$ and $∠ C$ id they are in the ratio $2 : 3$ .

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Solution

Let $∠ B$ and $∠ C$ be $2 x$ and $3 x$ respectively.

$∠ A = 50 ° (Given)$

From angle sum property of triangle,

$∠ A + ∠ B + ∠ C = 180 °$
$50 ° + 2 x + 3 x = 180 °$
$\Rightarrow 5 x = 180 ° - 50 °$
$\Rightarrow x = \frac{130 °}{5} = 26 °$

Therefore,
$∠ B = 2 x = 2 \times 26 ° = 52 °$
$∠ C = 3 x = 3 \times 26 ° = 78 °$

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∠ A = 30^{o}, ∠ B = 50^{o}, ∠ C = 80^{o}

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