The properties of triangles says the total of all three angles will always be 180 degrees. We can use this property to help build our equation for the problem.
Let l be the largest angle, m be the middle, and s be the smallest.
We know from the question that [tex]l = 2s - 30[/tex] and that [tex]m = s + 10[/tex].
From the property above, we know [tex]l + m + s = 180[/tex].
We then know [tex](2s - 30) + (s + 10) + s = 180[/tex]. From this, we can solve for s, and then plug that value into the equations above for l and m to find them.
Expand the parenthesis and combine like terms.
[tex]4s - 20 = 180[/tex]
Add 20 to each side.
[tex]4s = 200[/tex]
Divide both sides by 4.
[tex]s = 50[/tex]
So, our smallest angle is 50. Now recall the two equations for l and m above [tex]l = 2s - 30[/tex] and [tex]m = s + 10[/tex].
Plug in the value of s.
[tex]l = 2(50) - 30[/tex]
Multiply 2(50).
[tex]l = 100 - 30[/tex]
Subtract 30.
[tex]l = 70[/tex]
The value of the largest angle is 70.
Plug in the value of s.
[tex]m = 50 + 10[/tex]
Add 10.
[tex]m = 60[/tex]
Finally, the middle angle is 60. So the answers are l = 70, m = 60, and s = 50.
