Question 154571
Let x=measure of original angle, y=measure of the supplementary angle and z=measure of the complementary angle


Remember supplemental angles add to 180 degrees and complementary angles add to 90 degrees. So this means that {{{x+y=180}}} and {{{x+z=90}}}



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



{{{y=180-x}}} Subtract "x" from both sides.



{{{x+z=90}}} Move onto the second equation.



{{{z=90-x}}} Subtract "x" from both sides.




Since "measure of the supplement of an angle is 12 degrees greater than three times the measure of a complement" this means that the third equation is {{{y=3z+12}}}



{{{y=3z+12}}} Start with the third equation.



{{{180-x=3(90-x)+12}}} Plug in {{{y=180-x}}} and {{{z=90-x}}}



{{{180-x=270-3x+12}}} Distribute.



{{{180-x=-3x+282}}} Combine like terms on the right side.



{{{-x=-3x+282-180}}} Subtract {{{180}}} from both sides.



{{{-x+3x=282-180}}} Add {{{3x}}} to both sides.



{{{2x=282-180}}} Combine like terms on the left side.



{{{2x=102}}} Combine like terms on the right side.



{{{x=(102)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x=51}}} Reduce.



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Answer:


So the answer is {{{x=51}}} which means that the angle is 51 degrees