Question

In Figure, lines AB and CD intersect at O. If $∠$AOC+$∠$BOE=70° and $∠$BOD=40°, find $∠$BOE and reflex $∠$COE.

Answer 1

Given: $∠$AOC + $∠$BOE = 70° and $∠$BOD = 40°
To find: $∠$ BOE, and Reflex $∠$COE

From Figure,
($∠$AOC +$∠$BOE +$∠$COE) and ($∠$COE +$∠$BOD +$∠$BOE) forms a straight line.
So, $∠$AOC+$∠$BOE +$∠$COE = $∠$COE +$∠$BOD+$∠$BOE = 180°
Now, by putting the values of $∠$AOC + $∠$BOE = 70° and $∠$BOD = 40° we get
$∠$COE = 110° and $∠$BOE = 30°
So, reflex $∠$COE = 360o – 110o = 250o