Question 175903
Let x=given angle, y=supplement of angle x, and z=complement of angle x



Because "The supplement of an angle is 10deg. smaller than three times its complement.", this tells us that {{{y=3z-10}}}



Since "y" is the supplement to angle x, this means {{{x+y=180}}}. 



Also, since "z" is the complement to angle x, this means {{{x+z=90}}}. Solving for "z" and we get {{{z=90-x}}} 



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{{{x+y=180}}} Start with the second equation.



{{{x+3z-10=180}}} Plug in {{{y=3z-10}}} (the first equation)



{{{x+3(90-x)-10=180}}} Plug in {{{z=90-x}}} (the third equation)




Notice that after all of these substitutions, we end up with a simple equation with one unknown.



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So let's solve the equation:



{{{x+3(90-x)-10=180}}} Start with the given equation.



{{{x+270-3x-10=180}}} Distribute.



{{{-2x+260=180}}} Combine like terms on the left side.



{{{-2x=180-260}}} Subtract {{{260}}} from both sides.



{{{-2x=-80}}} Combine like terms on the right side.



{{{x=(-80)/(-2)}}} Divide both sides by {{{-2}}} to isolate {{{x}}}.



{{{x=40}}} Reduce.



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Answer:


So the answer is {{{x=40}}} which means that the given angle is 40 degrees.