Mathematics

Find the measure of an angle, if four times of its complement is $$12^o$$ more than twice the difference between its supplement and complement.


ANSWER

$$42$$


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 $$ 4\left( 90-x \right) =2\left[ \left( 180-x \right) -\left( 90-x \right)  \right] +12$$ 
$$ \Rightarrow 360-4x=2\times 90+12$$
$$\Rightarrow 360-4x=180+12\\ \Rightarrow 360-4x=192$$
$$\Rightarrow 4x=360-192$$
$$\Rightarrow 4x=168$$
$$\Rightarrow x=\dfrac { 168 }{ 4 }$$
$$ \Rightarrow x=42$$
Therefore, the angle is $$ { 42 }^{ o }$$.
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