Question

In figure, if AB ∥ CD, CD ∥ EF and y : z = 3 : 7, Find x.

• 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] $\cdots$ (i)
$\therefore y+z={180}^{\circ }$
Given: y : z = 3 : 7
Let y = 3k and z = 7k
$\Rightarrow 3k+7k={180}^{\circ }$
$\Rightarrow 10k={180}^{\circ }$
$\Rightarrow k={18}^{\circ }$

$\therefore z=7k=7\left(18\right)={126}^{\circ }$
Also, AB || CD
$\therefore \angle x=\angle CGH$ [Corresponding angles]
$\Rightarrow \angle x={126}^{\circ }$