Question

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

Answer 1

In given figure $AB$ is a straight line and $OC$ and $OE$ meets at point $O$ in $AB$.

$\angle AOC+\angle BOE+\angle COE={180}^{\circ }$

As given $\angle AOC+\angle BOE={70}^{\circ }$

$\therefore 70+\angle COE={180}^{\circ }$

$\Rightarrow \angle COE=180-70={110}^{\circ }$

Reflex $\angle COE={360}^{\circ }-{110}^{\circ }={250}^{\circ }$

$\because$ $CD$ is a straight line and $OE$ and $OB$ stand on it

$\angle COE+\angle BOE+\angle BOD={180}^{\circ }$

${110}^{\circ }+\angle BOE+{40}^{\circ }={180}^{\circ }$

$\angle BOE=180-110-40$

$\Rightarrow \angle BOE={30}^{\circ }$