Question

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

• A. $5:7$
• B. $3:5$
• C. $5:3$
• D. $1:1$

Answer 1

The correct option is D $1:1$

R.E.F image

As $AB\parallel CD\parallel EF$

$\Rightarrow x+y={180}^{\circ }$ (adjacent angles)

$\theta =z$ (opposite angles)

As $y:z=3:7=3r:7r$

and $y+\theta =y+z={180}^{\circ }$

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

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

$\Rightarrow y={54}^{\circ }\Rightarrow z={180}^{\circ }-y={126}^{\circ }$

& $x={180}^{\circ }-y={126}^{\circ }$

$\Rightarrow x:z=1:1$