Question

In the given figure, AC = CE and AB $\parallel$ ED. The value of $x$ is ___ units.

• A. 15
• B. 20
• C. 25
• D. 30

Answer 1

The correct option is A 15

$\text{In}\Delta ABC\text{and}\Delta EDC$,
AC = CE (given)
Also, AB$\parallel$DE and AE is a transversal.
$\Rightarrow \angle BAC=\angle DEC$ [alternate interior angles]
$\angle ACB=\angle ECD$ [vertically opposite angles]
$\therefore \Delta ABC\cong \Delta EDC$ (ASA congruence criterion)
$\Rightarrow AB=DE$ (CPCT)
$\Rightarrow x+10=2x-5$
$\Rightarrow x=15$ units