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.

$42$

##### 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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Single Correct Medium Published on 09th 09, 2020
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