Mathematics

In the figure, $$AOB$$ is a straight line, Find the value of $$x$$. Hence, find $$\angle AOC$$ and $$\angle BOD$$.


SOLUTION
From the figure we know that $$\angle AOB$$ is a straight line

So we get

$$\angle AOB={180}^{o}$$

It can also be written as

$$\angle AOC+\angle COD+\angle BOD={180}^{o}$$

By substituting the values

$${(3x-7)}^{o}+{55}^{o}+{(x+20)}^{o}={180}^{o}$$

$$3x-{7}^{o}+{55}^{o}+x+{20}^{o}={180}^{o}$$

On further calculate

$$4x+{180}^{o}={180}^{o}$$

$$4x={112}^{o}$$

$$x={28}^{o}$$

By substituting the value of $$x$$ we get

$$\angle AOC={(3x-7)}^{o}=3({28}^{o})-{7}^{o}$$

$$={84}^{o}-{7}^{o}={77}^{o}$$

$$\angle BOD={(x+20)}^{o}={(28+20)}^{o}={48}^{o}$$
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