Question

Find the unknown angle x in the figure.

• A. ${90}^{\circ }$
• B. ${125}^{\circ }$
• C. ${45}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is B

${125}^{\circ }$

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


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

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