Question

Find the unknown angle x in the figure.

(4 marks)

Answer 1

Draw a line CH passing through C, parallel to lines BG and DF

( 1 mark )

DF || CH || BG
$\Rightarrow a+b=x$
$a=\angle EDF={45}^{\circ }\dots \left(1\right)\left[\text{corresponding angles}\right]$
( 1 mark )
$b={180}^{\circ }-\angle GBC={180}^{\circ }-{100}^{\circ }={80}^{\circ }\dots \left(2\right)$
$\left[\text{Co-interior angles}\right]$
( 1 mark )

From (1) and (2), we get
$\Rightarrow x=a+b={45}^{\circ }+{80}^{\circ }={125}^{\circ }$
( 1 mark )