Mathematics

How many degrees are there in an angle which equals one-fifth of its supplement?


ANSWER

$$30^o$$


SOLUTION
Two angles which are supplementary add upto $$180$$ .....(1)
Let one angle be $$x$$ and other be$$\dfrac { 1 }{ 5 } x$$
Hence, $$x +\dfrac { 1 }{ 5 } x= 180$$ .....From (1)
$$ \Longrightarrow \dfrac { 6 }{ 5 } x = 180$$
$$\Longrightarrow x= 180 \times \dfrac { 5 }{ 6 }= 150$$ 
Thus one angle is $$150$$ and the other angle is $$\dfrac { 150 }{ 5 } =30^o$$.
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