Question

In the figure, if $AB\parallel CD,CD\parallel EF$ and $y:z=3:7$, find $x$.

Answer 1

Given,

$AB\parallel CD$ and $CD\parallel EF$

$y:z=3:7$

Now, $x+y={180}^{\circ }$ (Angles on the same side of transversal.)

Also, Let $\angle O=\angle Z$ (Corresponding angles)

and $\angle Y+\angle O={180}^{\circ }$ (Linear pair)

$\Rightarrow y+z={180}^{\circ }$

According to the question,

$y=3w$ and $z=7w$

$3w+7w={180}^{\circ }$

$\Rightarrow 10w={180}^{\circ }$

$\Rightarrow w={18}^{\circ }$

$\therefore y=3\times {18}^{\circ }={54}^{\circ }$

and $z=7\times {18}^{\circ }={126}^{\circ }$

Now, $x+y={180}^{\circ }$

$\Rightarrow x+{54}^{\circ }={180}^{\circ }$

$\Rightarrow x={126}^{\circ }$