In the adjoining figure, AB = 10 cm, BC =15 cm AD : DC = 2 : 3, then find the value of $∠$ ABC.

30º

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40º

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45º

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110º

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Solution

The correct option is B
40º

Clearly, $\frac{A D}{D C}$ = $\frac{2}{3}$ and $\frac{A B}{D C}$ = $\frac{10}{15}$ = $\frac{2}{3}$

So, $\frac{A D}{D C}$ = $\frac{A B}{B C}$

Thus, BD divides AC in the ratio of the other two sides.

$∴$ BD is the bisector of $∠$ B.

Now, $∠$ CBD = $180^{\circ}$ - ( $130^{\circ}$ + $30^{\circ}$ ) = $20^{\circ}$

$∠$ B = 2 ( $∠$ CBD)= $40^{\circ}$

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