Question

In the figure, AC || DF.
$\angle CBO={40}^{\circ }\text{and}\angle FEO={30}^{\circ }$
What is the value of the reflex angle $\angle BOE$?

Answer 1

To find the reflex $\angle BOE$, we first need to find the convex $\angle BOE$.

To find the convex $\angle BOE$, we draw a line PQ which is parallel to AC and DF passing through O.


Now, $\angle POE=\angle OEF$ (Alternate interior angles)

$\Rightarrow \angle POE={30}^{\circ }$ ----------- (1)

And, $\angle BOP=\angle OBC$ (Alternate interior angles)

$\Rightarrow \angle BOP={40}^{\circ }$ ----------- (2)

From (1) and (2),
$\angle BOE=\angle BOP+\angle POE={40}^{\circ }+{30}^{\circ }={70}^{\circ }$

Thus, the convex angle BOE is equal to ${70}^{\circ }$

Now, reflex angle BOE = ${360}^{\circ }-{70}^{\circ }={290}^{\circ }$