Question 215106
Let 


x = measure of unknown angle
y = measure of complement angle to angle 'x'
z = measure of supplement angle to angle 'x'



Since we know that 'x' and 'y' are complement angles (ie the angles add to 90 degrees), this means {{{x+y=90}}}. Likewise, 'x' and 'z' are supplement angles (the angles add to 180 degrees), so {{{x+z=180}}}.



Furthermore, we're told that we have an "angle whose supplement measures 20 more than twice its compliment" which means that {{{z=2y+20}}}



{{{x+y=90}}} Start with the first equation.



{{{y=90-x}}} Subtract x from both sides.
 

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{{{x+z=180}}} Move onto the second equation.



{{{z=180-x}}} Subtract x from both sides.


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{{{z=2y+20}}} Move to the third equation.



{{{z=2*highlight((90-x))+20}}} Plug in {{{y=90-x}}}



{{{highlight(180-x)=2(90-x)+20}}} Plug in {{{z=180-x}}}



{{{180-x=180-2x+20}}} Distribute.



{{{180-x=-2x+200}}} Combine like terms on the right side.



{{{-x=-2x+200-180}}} Subtract {{{180}}} from both sides.



{{{-x+2x=200-180}}} Add {{{2x}}} to both sides.



{{{x=200-180}}} Combine like terms on the left side.



{{{x=20}}} Combine like terms on the right side.



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Answer:


So the solution is {{{x=20}}} 



This means that the unknown angle is 20 degrees.



So the complement is {{{y=90-x=90-20=70}}} degrees



and the supplement is {{{z=180-x=180-20=160}}} degrees.