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Question

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

In given figure $$AB$$ is a straight line and $$OC$$ and $$OE$$ meets at  point $$O$$ in $$AB$$.

$$\angle AOC+\angle BOE+\angle COE=180^{\circ}$$

As given $$\angle AOC+\angle BOE=70^{\circ}$$

$$\therefore 70+\angle COE=180^{\circ}$$

$$\Rightarrow \angle COE=180-70=110^{\circ}$$

Reflex $$\angle COE=360^{\circ}-110^{\circ}=250^{\circ}$$

$$\because$$ $$CD$$ is a straight line and $$OE$$ and $$OB$$ stand on it

$$\angle COE+\angle BOE+\angle BOD=180^{\circ}$$

$$110^{\circ}+\angle BOE+40^{\circ}=180^{\circ}$$

$$\angle BOE=180-110-40$$

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

Mathematics
RS Agarwal
Standard IX

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