Question

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

Answer 1

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

Let $y=3a$ and $z=7a$

$\angle DHI=y$(vertically opposite angles)

$\angle DHI+\angle FIH={180}^{\circ }$ (Interior angles on the same side of the transversal)

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

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

$\Rightarrow 10a={180}^{\circ }$ or $a={18}^{\circ }$

$\therefore y=3\times {18}^{\circ }={54}^{\circ }$ and $z=7\times {18}^{\circ }={126}^{\circ }$

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

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

$\therefore x={180}^{\circ }-{54}^{\circ }={126}^{\circ }$

Hence,$x={126}^{\circ }$