Question

In the given figure, BE is parallel to CF. Evaluate the value of x.

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

Answer 1

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

Construction: Draw a line $OY$ passing through $O$, such that $OY\parallel BE\parallel CF$.

So, $BE||OY$ and AO is the transversal.

$\Rightarrow \angle BOY=\angle ABE$
(Since corresponding angles are equal)
$\Rightarrow \angle BOY=4x$

Similarly, $CF||OY$ and $CO$ is the transversal.

$\Rightarrow \angle COY=\angle DCF$
(Since corresponding angles are equal)
$\Rightarrow \angle COY=6x$

Now, $\angle BOC=\angle BOY+\angle COY$ (from the figure)

$\Rightarrow {130}^{\circ }=4x+6x$

$\Rightarrow 10x={130}^{\circ }$

$\Rightarrow x={13}^{\circ }$
Hence, B is the correct option.