Mathematics

Two lines $$AB$$ and $$CD$$ intersect at $$O$$. If $$\angle AOC={50}^{o}$$, find $$\angle AOD, \angle BOD$$ and $$\angle BOC$$


SOLUTION
From the figure we know that $$\angle AOC$$ and$$\angle AOD$$ from a linear pair

It can also be written as

$$\angle AOC+\angle AOD={ 180 }^{ o }$$

By substituting the values

$${50}^{o}+\angle AOD={ 180 }^{ o }$$

$$\angle AOD={ 180 }^{ o }-{50}^{o}$$

$$\angle AOD={130}^{o}$$

According to the figure we know that $$\angle AOD$$ and $$\angle BOC$$ are vertically opposite angles 

So we get

$$\angle AOD=\angle BOC={ 180 }^{ o }$$

According to the figure we know that $$\angle AOC$$ and $$\angle BOD$$ are vertically opposite angles

So we get

$$\angle AOC+\angle BOD={50}^{o}$$
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Subjective Medium Published on 09th 09, 2020
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