Mathematics

Find the measure of an angle, if five times of its complement is $$24^o$$ less than twice of its supplement.


ANSWER

$$38$$


SOLUTION
Two angles whose sum is $$ { 180 }^{ o }$$ are said to be supplementary.
Two angles whose sum is $$ { 90 }^{ o }$$ are said to be complementary.
Let the angle be $$ x$$.
Given that $$ 5\left( 90-x \right) =2\left( 180-x \right) -24$$
$$ \Rightarrow 450-5x=360-2x-24\\ \Rightarrow 5x-2x=450-360+24\\ \Rightarrow 3x=474-360$$
$$\Rightarrow 3x=114\\ \Rightarrow x=\dfrac { 114 }{ 3 } $$
$$\Rightarrow x=38\\ $$
Therefore, the angle is $$ { 38 }^{ o }$$.
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