In the given figure, $∠ B : ∠ C = 2 : 3$ , Find $∠ B$

120^{\circ}

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52^{\circ}

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78^{\circ}

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130^{\circ}

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Solution

The correct option is B $52^{\circ}$
R.E.F image
$∠ O A C + ∠ C A B = 180^{0}$
$∠ C A B = 50^{0}$
$∠ B = x [i . e . x]$
$\frac{∠ B}{∠ C} = \frac{2}{3}$
$∠ C = \frac{3 x}{2}$
Triangular Property
$∠ A + ∠ B + ∠ C = 180^{0}$
$50 + x + \frac{3 x}{2} = 180$
$\frac{5 x}{2} = 130$
$x = 52^{0}$
$∠ B = 52^{0}$

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