Question

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

• A. ${137}^o$
• B. ${126}^o$
• C. ${150}^o$
• D. ${176}^o$

Answer 1

The correct option is B ${126}^o$

$AB\parallel CD$ and $CD\parallel EF$

Therefore, $AB\parallel EF$

$\therefore x=z$ [Alternate interior angles] ....(1)

Again, $AB\parallel CD$

$x+y={180}^o$ [Co-interior angles]

$z+y={180}^o$ .......(2) [From 1]

But, $y:z=3:7$

$z=\frac{7}{3}y=\frac{7}{3}({180}^o-z)$ [By using 2]

$10z=7\times 180$

$z={126}^o$

Thus, $x={126}^o$