In the given figure, AC = CE and AB||ED. Using this information, find the value of $x$ .

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Solution

The correct option is B 15
In $Δ$ ABC and $Δ$ EDC,

AC = CE .... (Given)

$∠ B A C = ∠ D E C$ (Alternate angles)

$∠ A C B = ∠ E C D$
(Vertically opposite angles)

$∴ Δ A B C ≅ Δ E D C$
(by ASA congruence criteria)

$\Rightarrow A B = D E$ (corresponding sides of congruent triangles)

$\Rightarrow x + 10 = 2 x - 5$

$\Rightarrow x = 15$

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