Question 219641
"two angles are supplementary." means that they form a straight line and they add to 180 degrees. Since "One angle has a measure of 5x+40 and the other has a measure of 2x." and we know that these angles are supplementary, this means:


{{{(5x+40)+(2x)=180}}}



{{{5x+40+2x=180}}} Remove the parenthesis.



{{{7x+40=180}}} Combine like terms on the left side.



{{{7x=180-40}}} Subtract {{{40}}} from both sides.



{{{7x=140}}} Combine like terms on the right side.



{{{x=(140)/(7)}}} Divide both sides by {{{7}}} to isolate {{{x}}}.



{{{x=20}}} Reduce.



Now just plug this value back into the given angles: 


Angle 1: {{{5x+40=5(20)+40=100+40=140}}}


Angle 2: {{{2x=2(20)=40}}} 



So the second angle is the smaller angle which is 40 degrees.