Question

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

(3 marks)

Answer 1

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

AC = CE .... (Given)

$\angle BAC=\angle DEC$ (Alternate angles)
(0.5 mark)
$\angle ACB=\angle ECD$
(Vertically opposite angles) (0.5 mark)
$\therefore \Delta ABC\cong \Delta EDC$
(by ASA congruence criteria) (0.5 mark)
$\Rightarrow AB=ED$ (corresponding sides of congruent triangles) (0.5 mark)
$\Rightarrow x+10=2x-5$

$\Rightarrow x=15$ (1 mark)