Question

In the figure, lines $AB$ and $CD$ intersect at $O$. If $\angle AOC+\angle BOE={70}^{\circ }$ and $\angle BOD={40}^{\circ }$, find $\angle BOE$ and reflex $\angle COE$.

Answer 1

In the figure,$AB$ and $CD$ intersect each other at $O$
$\angle AOC+\angle BOE={70}^{\circ }$ and $\angle BOD={40}^{\circ }$
Now, $AB$ is a line
$\therefore \angle AOC+\angle BOE+\angle COE={180}^{\circ }$
(Angles on a line are supplementary)
$\Rightarrow {70}^{\circ }+\angle COE={180}^{\circ }$
$\Rightarrow \angle COE={180}^{\circ }-{70}^{\circ }={110}^{\circ }$
Also, $\angle AOC=\angle BOD$ (Vertically opposite angles)
$\Rightarrow \angle AOC={40}^{\circ }$
$\therefore \angle BOE={70}^{\circ }-{40}^{\circ }={30}^{\circ }$
Hence, relfex $\angle COE={360}^{\circ }-\angle COE$
= ${360}^{\circ }-{110}^{\circ }={250}^{\circ }$