Mathematics

# In Fig., lines AB and CD intersect at O. If $\angle AOC+\angle BOE= 70^{\circ}$ and $\angle BOD= 40^{\circ}$, find $\angle BOE$ in degrees.

30

##### SOLUTION
We have,
$\angle BOD= 40^{\circ}$

$\Rightarrow \angle AOC= 40^{\circ}$     $[\because \angle AOC= \angle BOD$ (vertically opposite angles)]

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

$\Rightarrow 40^{\circ}+\angle BOE= 70^{\circ}\Rightarrow \angle BOE= 30^{\circ}$

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