Question

In the given figure, AC = CE and AB || ED. The value of x is . (2 marks)

Answer 1

In $\Delta$ ABC and $\Delta$ EDC
AC = CE .... (Given)
$\angle BAC=\angle DEC$.... (Alternate angles)
$\angle ACB=\angle ECD$ .... (Vertically opposite angles)
$\therefore \Delta ABC\cong \Delta EDC$ .... (ASA congruence criteria)
(1 mark)
$\Rightarrow AB=DE$ ..... (Sides of congruent triangles)
$\Rightarrow x+10=2x-5$
$\Rightarrow x=15units$
(1 mark)