Question

In the given figure, $BE$ is parallel to $CF$. What will the value of $x$ be?

• A. ${23}^{\circ }$
• B. ${65}^{\circ }$
• C. ${13}^{\circ }$
• D. ${12}^{\circ }$

Answer 1

The correct option is C ${13}^{\circ }$

Construction: Draw a line $XY$ such that $XY||BE||CF$ and is passing through $O$.

So, $BE||XY$ and $AO$ is the transversal.
$\Rightarrow \angle BOY=\angle ABE$ (Corresponding angles are equal.)
$\Rightarrow \angle BOY=4x$

Similarly, $CF||XY$ and $CO$ is the transversal.
$\Rightarrow \angle COY=\angle DCF$ (Since corresponding angles are equal)
$\Rightarrow \angle COY=6x$

Now, $\angle BOC=\angle BOY+\angle COY$
$\Rightarrow {130}^{\circ }=4x+6x$
$\Rightarrow {130}^{\circ }=10x$
$\Rightarrow x=\frac{130}{10}$
$\Rightarrow x={13}^{\circ }$