Question

Question 1
In the given figure, lines AB and CD intersect at O. if $\angle AOC+\angle BOE=70and\angle BOD={40}^{\circ },find\angle BOE$ and reflex $\angle COE.$

Answer 1

AB is straight line, rays OC and OE stand on it.
$\angle AOC+\angle COE+\angle BOE={180}^{\circ }$
$(\angle AOC+\angle BOE)+\angle COE={180}^{\circ }$
${70}^{\circ }+\angle COE={180}^{\circ }$
$\angle COE={180}^{\circ }-{70}^{\circ }={110}^{\circ }$
$Reflex\angle COE={360}^{\circ }-{110}^{\circ }={250}^{\circ }$
CD is a straight line, rays OE and OB stand on it.
$\angle COE+\angle BOE+\angle BOD={180}^{\circ }$
$\Rightarrow {110}^{\circ }+\angle BOE+{40}^{\circ }={180}^{\circ }$
$\Rightarrow \angle BOE={180}^{\circ }-{150}^{\circ }={30}^{\circ }$