Mathematics

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

$38$

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