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.


ANSWER

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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