Question

From the diagram, if $AB$ and $CD$ are parallel to each other, then the value of reflex $\angle EOF$ is

• A. ${210}^{\circ }$
• B. ${210}^{\circ }$
• C. ${235}^{\circ }$

Answer 1

The correct option is A ${210}^{\circ }$

Let's draw a line $PQ$ paralle to $AB$ and passing through $O$.
Now, $\angle AFO$ and $POF$ are alternate interior angles.
$\Rightarrow \angle AFO=\angle POF={120}^{\circ }$
Also, $\because \angle OEC$ is a right angle.
$\Rightarrow \angle POE=\angle OEC={90}^{\circ }$ (alternate interior angles)
Now, $\angle POF={120}^{\circ }$ and $\angle POE={90}^{\circ }$
$\therefore$ reflex $\angle EOF={90}^{\circ }+{120}^{\circ }={210}^{\circ }$