Mathematics

In the given figure, two lines $$AB$$ and $$CD$$ intersect at $$O$$. Ray $$OE$$ is perpendicular to the line $$AB$$. If $$a:b=3:7,$$ then find reflex $$\angle BOD$$.


SOLUTION
In the given figure,

We have,

$$a:b=3:7$$

$$\angle EOA=90^o$$

Let $$a=3x , b=7x$$

Since,
$$ \angle EOC+\angle BOC +\angle EOA=180^o$$

$$3x+7x+90^o=180^o$$

$$x=9^o$$


Thus $$a=27^o$$ and $$b=63^o$$

Now,

$$=\angle AOB+\angle BOD$$

$$=63^o+\angle BOD=180^o$$

$$=\angle BOD=117^o$$
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