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

Lines AB and CD intersect at O.

$\angle AOC=\angle BOD$ [Vertically opposite angles]

But $\angle BOD={40}^{\circ }$ ..(i) [given]

$\angle AOC={40}^{\circ }$ ..(ii)

Now,$\angle AOC+\angle BOE={70}^{\circ }$ [Given]

${40}^{\circ }+\angle BOE={70}^{\circ }$ [Using (ii)]

$\angle BOE={70}^{\circ }-{40}^{\circ }$

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

$Reflex\angle COE=\angle COD+\angle BOD+\angle BOE)$

$Reflex\angle COE={180}^{\circ }+{40}^{\circ }+{30}^{\circ }$

$Reflex\angle COE={250}^{\circ }$