Question

In the figure, if AB ∥ CD, CD ∥ EF and $y:z=3:7$, then the value of $x$ is:

• A. ${112}^{\circ }$
• B. ${116}^{\circ }$
• C. ${96}^{\circ }$
• D. ${126}^{\circ }$

Answer 1

The correct option is D ${126}^{\circ }$

Given, CD || EF
$\Rightarrow \angle CGH=\angle FHG$ [Alternate interior angles]
$\Rightarrow \angle CGH=z$

Also,
$\angle CGI+\angle CGH={180}^{\circ }$ [Linear pair]
$\therefore y+z={180}^{\circ }$

Given: $y:z=3:7$
Let $y=3k$ and $z=7k$ for some $kϵR$
then, $y+z={180}^{\circ }$
$\Rightarrow 3k+7k={180}^{\circ }$
$\Rightarrow 10k={180}^{\circ }$
$\Rightarrow k={18}^{\circ }$

$\therefore z=7k=7\left(18\right)={126}^{\circ }$

Also, AB || CD
$\therefore \angle x=\angle CGH$ [Corresponding angles]
$\Rightarrow \angle x={126}^{\circ }$