Question 183256
Let x=unknown angle

So the supplement is 180-x and the compliment is 90-x


This means that "The measure of the angle's supplement is 40 degrees more than 3 times that of its complement" translates to {{{180-x=3(90-x)+40}}}



{{{180-x=3(90-x)+40}}} Start with the given equation.



{{{180-x=270-3x+40}}} Distribute.



{{{180-x=-3x+310}}} Combine like terms on the right side.



{{{-x=-3x+310-180}}} Subtract {{{180}}} from both sides.



{{{-x+3x=310-180}}} Add {{{3x}}} to both sides.



{{{2x=310-180}}} Combine like terms on the left side.



{{{2x=130}}} Combine like terms on the right side.



{{{x=(130)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x=65}}} Reduce.



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Answer:


So the answer is {{{x=65}}} which means that the unknown angle is 65 degrees.