Question 205783
First we will start out assigning variables
x = shortest side
y = middle side
z = longest side

1.Because all the interior angles of a triangle have to add up to 180 be can write the following equation
- {{{x+y+z=180}}}
2. Next we write tow additional equations dealing with each variable independantly
3. Because we want to solve for the longest side, z , then we need to write two equations, one where x is by itself (in fancy terms, x in terms of z), and the other where y is by itself (y in terms of z)
- {{{y=(1/3)z}}}
- {{{y=2x}}}
a. Becuase the problem doesn't describe z in terms of x we will have to make one by substituting
b. because {{{y=(1/3)z}}} we can substitue that value into this equation {{{ y=2x}}}
- {{{y=(1/3)z}}} 
- {{{2x = (1/3)z}}}
c. Now solve for x
- {{{2x = (1/3)z}}}
- {{{(2x)/2 = (1/3)z(1/2)}}}
- {{{x = (1/6)z}}}
d. Now we have the two equations
- {{{y=(1/3)z}}}
- {{{x = (1/6)z}}}
3. Now substitute those equations back into the first equation
- {{{x+y+z=180}}}
- {{{((1/6)z) + ((1/3)z) + z = 180}}}
4. Finally solve for z
- {{{((1/6)z) + ((1/3)z) + z = 180}}}
- {{{(1/6)z+(2/6)z+(6/6)z = 180}}}
- {{{(9/6)z = 180}}}
- {{{(6/9)(9/6)z = (6/9)180}}}
- {{{z = 1080/9}}}
- {{{z = 120}}}
5. So the largest angle is 120 degrees
--Check--
{{{y=(1/3)z}}}
{{{y=120/3}}}
{{{y=40}}}
{{{x=(1/6)z}}}
{{{x=120/6}}}
{{{x=20}}}
{{{20+40+120 = 180}}}
{{{180 = 180}}}