Question

In the adjacent figure AB || CD; CD || EF and y : z = 3 : 7, find x.

Answer 1

Let $y$ and $z$ be $3u$ and $7u$

$\angle x=\angle z$ (Alternate angles)

$\angle x+\angle y={180}^{\circ }$ (Angles made on same side of transversal)

Put $x=z$

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

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

$10u={180}^{\circ }$

$u=\frac{{180}^{\circ }}{10}={18}^{\circ }$

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

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