Question

Question 2
In the given figure, If $AB||CD,CD||EF$ and $y:z=3:7$, find x.

Answer 1

It is given that $AB||CDandCD||EF$.
Then. $AB||CD||EF$.
$\Rightarrow AB||EF$ (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.
$3a+7a={180}^{\circ }$
$10a={180}^{\circ }$
$a=\frac{{180}^{\circ }}{10}$
$a={18}^{\circ }$
$\therefore x=z=7a=7\times {18}^{\circ }={126}^{\circ }$