Question

In the given figure, Line $AB\parallel$ line $CD\parallel$ line $EF$ and line $QP$ is their transversal. If $y:z=3:7$ then find the measure of $\angle x$.

Answer 1

$y:z=3:7$ [Given]
Let the common multiple be $m$
$\therefore \angle j=3m$ and $\angle Z=7m$....(i)
line $AB$ || line $EF$ and line $PQ$ is their transversal [Given]
$\angle X=\angle Z$
$\therefore \angle x=7m$.....(ii) [From (i)]
line $AB\parallel$ line $CD$ and line $PQ$ is their transversal [Given]
$\angle x+\angle y={180}^{\circ }$
$\therefore 7m+3m={180}^{\circ }$
$\therefore 10m={180}^{\circ }$
$\therefore m={18}^{\circ }$
$\therefore \angle x=7m=7\left({18}^{\circ }\right)$ [From (ii)]
$\therefore \angle x={126}^{\circ }$