Question

In the given figure, $AB\parallel CD$. Find $x$.

• A. ${26}^o$
• B. ${13}^o$
• C. ${23}^o$
• D. ${46}^o$

Answer 1

The correct option is B ${13}^o$

Through point $E$ draw a line $EF$ parallel to $CD$ and $AB$
Now, $\angle CEF=4x$ ($CD\parallel EF$, corr. $\angle s$)
$\angle AEF=6x$($EF\parallel AB$, corr. $\angle s$)
Given, $\angle CEA={130}^o$ $\Rightarrow$ $\angle CEF+\angle AEF={130}^o$
$\Rightarrow$ $4x+6x={130}^o$ $\Rightarrow$ $10x={130}^o$
$\Rightarrow$ $x={13}^o$