Question

In the given figure $AB$ ∥ $CD$, $\angle AEO={55}^{\circ }$, $\angle CFO={40}^{\circ }$. The measure of reflex $\angle EOF$ is

• A. ${285}^{\circ }$
• B. ${290}^{\circ }$
• C. ${265}^{\circ }$

Answer 1

The correct option is C ${265}^{\circ }$

Construct a line $XOY$ ∥ $AB$.
Since $XY$ ∥ $AB$, $\angle EOY=\angle AEO={55}^{\circ }$
(interior opposite angles are equal)
$\therefore \angle EOY={55}^{\circ }$
Since $XY$ ∥ $CD$, $\angle CFO=\angle FOY={40}^{\circ }$ (interior opposite angles are equal)
$\Rightarrow \angle EOF=\angle EOY+\angle FOY$
$\Rightarrow \angle EOF={55}^{\circ }+{40}^{\circ }={95}^{\circ }$
Now, reflex $\angle EOF={360}^{\circ }-{95}^{\circ }={265}^{\circ }$