Question 907108
Step 1.  Two angles are complementary when they add up to {{{90}}} degrees and two angles are supplementary when they add up to {{{180}}} degrees


Step 2.  Let {{{x}}} be the angle.


Step 3.  Let {{{90-x}}} be the complementary angle.


Step 4.  Let {{{180-x}}} be the supplementary angle.


Step 5.  Let {{{5(90-x)}}} be five times the complement of the angle.


Step 6.  Let {{{2(180-x)}}} be twice the measure of its supplement


Step 7.  Let {{{5(90-x)=2(180-x)-24}}}  since  five times the measure of its complement is {{{24}}} less than twice the measure of its supplement
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Step 8.  Then solving the equation of Step 7 {{{5(90-x)=2(180-x)-24}}} will lead to the following steps:


{{{5(90-x)=2(180-x)-24}}} ....solve for {{{x}}}

{{{450-5x=360-2x-24}}}

{{{450-5x=336-2x}}}

{{{450-336=5x-2x}}}

{{{114=3x}}}

{{{114/3=x}}}

{{{38=x}}}



So {{{x=38}}} and {{{90-x=52}}} and {{{180-x=142}}}.


Check...{{{5(x-90)=2(x-180)-24}}} if true than {{{5*52=2*142-24}}} =>{{{260=260}}} which is a true statement.


 ANSWER:  
The angle is {{{38}}} degrees, its complementary angle is {{{52}}} degrees and its supplementary angle is {{{142}}} degrees.