Question

In a hexagon $ABCDEF$; side $AB$ is parallel to side $FE$ and $\angle B:\angle C:\angle D:\angle E=6:4:2:3.$

Find the measure of $\angle B$.

• A. ${108}^{\circ }$
• B. ${216}^{\circ }$
• C. ${244}^{\circ }$
• D. None of these

Answer 1

The correct option is B ${216}^{\circ }$

Given in hexagon $ABCDEF$

And $\angle B:\angle C:\angle D:\angle E=6:4:2:3$

Let $\angle B=6x,\angle C=4x,\angle D=2x,\angle E=3x$

Now $AB||EF$ and $AF$ is the traversal.

$\Rightarrow \angle A+\angle F={180}^0$ (Linear pair)

Now hexagon has $6$ sides

Sum of angle of hexagon $=(6-2)\times 180$

$\Rightarrow \angle A+\angle B+\angle C\angle D+\angle E+\angle F=4\times 180$

$\Rightarrow 180+6x+4x+2x+3x=720$

$\Rightarrow 15x=720-180$

$\Rightarrow 15x=540$

$\Rightarrow x={36}^0$

Hence, $\angle B=6\times 36={216}^0$