Question 207726
Let 


A = measure of angle A
c = measure of complement angle
s = measure of supplement angle



"The complement of angle A is 20 degrees less than half the supplement of angle A" literally translates to the equation {{{c=(1/2)s-20}}}



Also, by definition, since 'c' is the complement to angle A, this means that they add to 90 degrees. So {{{A+c=90}}}


Furthermore, supplemental angles add to 180 degrees. Because 's' is the supplement to angle A, we know that {{{A+s=180}}}



{{{A+c=90}}} Start with the second equation.



{{{c=90-A}}} Subtract A from both sides.



{{{A+s=180}}} Move onto the second equation



{{{s=180-A}}} Subtract A from both sides.



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{{{c=(1/2)s-20}}} Now move back to the first equation.



{{{90-A=(1/2)s-20}}} Plug in {{{c=90-A}}}



{{{90-A=(1/2)(180-A)-20}}} Plug in {{{s=180-A}}}



{{{90-A=(1/2)(180)-(1/2)A-20}}} Distribute



{{{90-A=180/2-(1/2)A-20}}} Multiply



{{{90-A=90-(1/2)A-20}}} Reduce



{{{2(90)-2(a)=2(90)-cross(2)((1/cross(2))a)-2(20)}}} Multiply EVERY term by the LCD {{{2}}} to clear any fractions.



{{{180-2a=180-1a-40}}} Multiply and simplify.



{{{180-2a=-a+140}}} Combine like terms on the right side.



{{{-2a=-a+140-180}}} Subtract {{{180}}} from both sides.



{{{-2a+a=140-180}}} Add {{{a}}} to both sides.



{{{-a=140-180}}} Combine like terms on the left side.



{{{-a=-40}}} Combine like terms on the right side.



{{{a=(-40)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{a}}}.



{{{a=40}}} Reduce.



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Answer:


So the solution is {{{a=40}}} 



This means that the original angle is 40 degrees while the complement is {{{c=90-40=50}}} degrees and the supplement is {{{s=180-40=140}}} degrees.