Question 212985
the supplement of an angle is four times the complement of the angle. Find the measure of the complement.


Let the angle be A
Then the supplement of the angle is (180 - A), and the complement of the angle is (90 - A)


Since the supplement is four times the complement, then we'll have:


180 - A  =  4(90 - A)


180 - A = 360 - 4A


3A  =  180


{{{A = 180/3 = 60^o}}}


Since A, or the angle is {{{60^o}}}, then its complement is 90 - 60 = {{{highlight_green(30^o)}}} 

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Check
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Angle = {{{60^o}}}. Therefore, its supplement = {{{120^o}}} (180 - 60)

Also, its complement is {{{30^o}}} (90 - 60)

So, since its supplement is equal to 4 times its complement, then:

{{{120^o = 4(30)}}}, or, {{{120^o = 120^o}}} ---TRUE---