Question

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

Answer 1

In $\Delta$ABC and $\Delta$EDC,

AC = CE .... (Given)

$\angle BAC=\angle DEC$ (Alternate angles)

$\angle ACB=\angle ECD$
(Vertically opposite angles)

$\therefore \Delta ABC\cong \Delta EDC$
(by ASA congruence criteria)

$\Rightarrow AB=DE$ (corresponding sides of congruent triangles)

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

$\Rightarrow x=15$