Question 147584
First, set a variable for the smallest angle. How about x?  So according to the question, the values for the angles in terms of x would be x, 3x, and 2(3x+x).  The angles of a triangle add up to 180 degrees, so set up an equation like this{{{x+3x+2(3x+x)=180}}}  Then distribute the two and get {{{x+3x+6x+2x=180}}}.  Then combine like terms and get {{{12x=180}}} and then divide both sides by 12 and get {{{x=180/12}}} which reduces to 15. That is the smallest angle. To get the largest angle, plug in 15 for x in the original value that you assigned to that angle ({{{2(3x+x)}}}).  You should get {{{2(45+15)}}} or {{{2(60)}}}.  That is 120. So the biggest angle is 120.  


To check, plug in 15 for all the x's in the original equation {{{x+3x+2(3x+x)=180}}}.  You should get {{{15+45+120}}}, or 120+60, which is 180, so it all works out.


The angle measures are 120, 45, and 15.