Question

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

Answer 1

$\text{In}\Delta ABC\text{and}\Delta EDC,AC=CE\text{(given)}\angle BAC=\angle DEC\text{(since AB||DE and AE is a transversal, so they are alternate angles)}\angle ACB=\angle ECD\text{(vertically opposite angles)}\therefore \Delta ABC\cong \Delta EDC\text{(A.S.A. congruence criteria)}\therefore AB=DE\text{(sides of congruent triangles)}\therefore x+10=2x-5\Rightarrow x=15units$