Mathematics

Two adjacent angles on a straight line are in the ratio $$5:4$$. Find the measure of each one of these angles.


SOLUTION
Consider the two adjacent angles as $$5x$$ and $$4x$$

We know that the two adjacent angles form a linear pair

So it can be written as

$$5x+4x={ 180 }^{ o }\Rightarrow 9x={ 180 }^{ o }$$

$$x={20}^{o}$$

substituting the value of $$x$$ in two adjacent angles

$$5x=5(20)={100}^{o}$$

$$4x=4(20)={80}^{o}$$

Therefore the measure of each one these angles is $${100}^{o}$$ and $${80}^{o}$$
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