Question 221104
Remember, all angles in a triangle add to 180 degrees. This means {{{(6n+31)+(5n-19)+(n+12)=180}}}



{{{(6n+31)+(5n-19)+(n+12)=180}}} Start with the given equation.



{{{6n+31+5n-19+n+12=180}}} Remove the parenthesis.



{{{12n+24=180}}} Combine like terms on the left side.



{{{12n=180-24}}} Subtract {{{24}}} from both sides.



{{{12n=156}}} Combine like terms on the right side.



{{{n=(156)/(12)}}} Divide both sides by {{{12}}} to isolate {{{n}}}.



{{{n=13}}} Reduce.




Now just plug this value into the given angles to get:


{{{6n+31=6(13)+31=78+31=109}}}



{{{5n-19=5(13)-19=65-19=46}}}



{{{n+12=13+12=25}}}



So the three angles are 109, 46, and 25 degrees.