Question

In the figure (not drawn to scale). $DAE,CBH$ and $ACG$ are straight lines, $DAE\parallel CBH\parallel FG$. Find $x$ and $y$ respectively.

• A. ${70}^{\circ },{35}^{\circ }$
• B. ${110}^{\circ },{145}^{\circ }$
• C. ${110}^{\circ },{35}^{\circ }$
• D. ${140}^{\circ },{20}^{\circ }$

Answer 1

The correct option is B ${110}^{\circ },{145}^{\circ }$

Since, $FG\parallel DAE$ and $AG$ is transversal.
$\therefore \angle FGA+\angle DAG={180}^{\circ }$ (Co-interior angles)
$\Rightarrow {70}^{\circ }+\angle x={180}^{\circ }\Rightarrow \angle x={110}^{\circ }$
Also, $CBH\parallel DAE$ and $BA$ is transversal.
$\angle y+\angle 35={180}^{\circ }$ (Co-interior angles)
$\Rightarrow \angle y={180}^{\circ }-{35}^{\circ }\Rightarrow \angle y={145}^{\circ }$.