Mathematics

The ratio between two complementary angles is $$2 : 3$$: find the smallest angle.


ANSWER

$$36$$


SOLUTION
Two angles whose sum is $$ { 90 }^{ o }$$ are said to be complementary. 
Given two angles are in the ratio of $$ 2:3$$.
Let the two angles be $$ 2x$$ and $$ 3x$$. 
So, $$\ 2x+3x={ 90 }^{ o }$$
$$\Rightarrow 5x={ 90 }^{ o }$$ 
$$\Rightarrow x=\dfrac { 90 }{ 5 } $$
$$\Rightarrow x=18\\$$ 
Therefore, the two angles are $$ 2x={ 36 }^{ o }$$ and $$ 3x={ 54 }^{ o }
$$.
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