Question

In fig, AB and CD are parallel to each others. The value of $x$ is :

• A. ${90}^{\circ }$
• B. ${100}^{\circ }$
• C. ${120}^{\circ }$
• D. ${140}^{\circ }$

Answer 1

The correct option is B ${100}^{\circ }$

Draw a line parallel to $AB$ and $CD$ and passing through $E$ as shown in the figure which divides $x$ in $\angle 1$ and $\angle 2$

Now $AB||EF$ and ang $BE$ is transversal

$\therefore \angle 1+{120}^{\circ }={180}^{\circ }$ (Sum of angles made on side side of transversal is supplementary)

$\Rightarrow \angle 1={180}^{\circ }-{120}^{\circ }\Rightarrow \angle 1={60}^{\circ }$

Also $DC||EF$ and $DE$ is transversal

$\therefore \angle 2+{140}^{\circ }={180}^{\circ }$ (Sum of angles made on side side of transversal is supplementary)

$\Rightarrow \angle 2={180}^{\circ }-{140}^{\circ }\Rightarrow \angle 1={40}^{\circ }$

$x=\angle 1+\angle 2\Rightarrow x={60}^{\circ }+{40}^{\circ }={100}^{\circ }$