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Equal Angles Subtend Equal Sides

In the given ...

Question

In the given figure, $D E ∥ B C .$
$A D = x, D B = x - 2$
$A E = x + 2, E C = x - 1$
What is the value of $x ?$

3

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Solution

The correct option is B $4$
Given, $D E ∥ B C$
Now, by Basic Proportionality theorem
$\frac{A D}{D B} = \frac{A E}{E C}$
$\Rightarrow \frac{x}{x - 2} = \frac{x + 2}{x - 1}$
$\Rightarrow x^{2} - x = x^{2} - 4$
$\Rightarrow x = 4$

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