Question

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

Answer 1

It is given that $AB\parallel CD$ and $CD\parallel EF$

$\Rightarrow AB\parallel CD\parallel EF$ (Lines parallel to the same line are parallel to each other)

It can be observed that

$x=z$ (Alternate interior angles) … (1)

It is given that, $y:z=3:7$

Let the common ratio between $y$ and $z$ be $a$.

$\Rightarrow y=3a$ and $z=7a$

Also, $x+y={180}^{\circ }$ (Co-interior angles on the same side of the transversal)

$\Rightarrow z+y={180}^{\circ }$ [Using equation (1)]

$\Rightarrow 7a+3a={180}^{\circ }$

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

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

Now,

$x=7a=7\times {18}^{\circ }={126}^{\circ }$