Question

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

• A. $\angle COE={30}^o$
• B. $\angle BOE={30}^o$
• C. $\angle BOE={110}^o$
• D. $\angle COE={110}^o$

Answer 1

Answer: (B), (D)

The correct options are
B $\angle BOE={30}^o$
D $\angle COE={110}^o$

From figureAOC=BOD [Vertically opposite angles]
AOC=${40}^o$[BOD=${40}^o$ is given]
Now, AOC+BOE=${70}^o$ [Given]
${40}^o+BOE={70}^o$
$BOE={30}^o$
$AOE+BOE={180}^o$ [Linear pair of angles]
$AOE+{30}^o={180}^o$
$AOE={150}^o$
$AOC+COE={150}^o$
${40}^o+COE={150}^o$
$COE={110}^o$