Mathematics

Find smallest of two supplementary angles, if they are in the ratio $$7 : 11$$.


ANSWER

$$70$$


SOLUTION
Two angles whose sum is $$ { 180 }^{ o }$$ are said to be supplementary.
Given two angles are the ratio of $$ 7:11$$ 
Let the two angles be $$7x$$ and $$ 11x$$.
So, $$ 7x+11x={ 180 }^{ o }$$
$$\Rightarrow 18x={ 180 }^{ o }$$
$$\Rightarrow x=\dfrac { 180 }{ 18 }$$
$$ \Rightarrow x={ 10 }$$
Therefore, the two angles are $$ 7x={ 70 }^{ o }$$ and $$ 11x={ 110 }^{ o }
$$.
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