Question

In the given figure, if $CD$ is parallel to $GE$ and $AB$ is parallel to GH, find the value of $y$.

• A. ${10}^{\circ }$
• B. ${15}^{\circ }$
• C. ${20}^{\circ }$
• D. ${25}^{\circ }$

Answer 1

The correct option is A ${10}^{\circ }$


Given, $DC$ is parallel to $GE$ and $AB$ is parallel to $GH$.
Now, $\angle ADC$ and $\angle DFE$ are corresponding angles.
$\Rightarrow \angle ADC=\angle DFE\text{(CD is parallel to GE.)}$
$\Rightarrow \angle DFE={120}^{\circ }$
Now, $\angle DFE$ and $\angle EFB$ are lying on the same line.
$\Rightarrow \angle EFB+\angle DFE={180}^{\circ }$
$\Rightarrow \angle EFB=180-120={60}^{\circ }$

We know that $AB$ is parallel to $GH.$
$\Rightarrow \angle EFB=\angle FGH={60}^{\circ }$ (Corresponding angles)
$\Rightarrow 3y+30={60}^{\circ }$
$\Rightarrow 3y=30$
$\Rightarrow y={10}^{\circ }$