In the following diagram,
$∠$ B : $∠$ C = 2 : 3. Find $∠$ C

{(\frac{339}{5})}^{\circ}

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{(\frac{309}{5})}^{\circ}

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{(\frac{369}{5})}^{\circ}

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{(\frac{319}{5})}^{\circ}

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Solution

The correct option is B ${(\frac{309}{5})}^{\circ}$
$∠ B : ∠ C = 2 : 3$
Let $∠ B = 2 x, ∠ C = 3 x$
$∠ B + ∠ C = 103$
$2 x + 3 x = 103$
$x = \frac{103}{5}$
Hence, $∠ C = 3 x = 3 \times \frac{103}{5} = \frac{309}{5}$

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