Question 159254: The angles of a triangle are three consecutive even integers. What is the largest angle in the triangle?
Answer by t_as87(5)   (Show Source):
You can put this solution on YOUR website! Your first clue to a 1st equation is that you have a triangle, we know the sum of the angles of a triangle is 180. We also know that the angles are consecutive... ie. They come one after the other.
So if A, B, C represent the 3 integers being the angles of the triangle, we know that B = A + 1, and C = A + 2
(Think of 1,2,3... 2 = 1+1, and 3 = 1 + 2)
We also know that A + B + C = 180
So we can set up the following equation
A + (A + 1) + (A + 2) = 180
Now solve for A
3A + 3 = 180
3A = 177
so A = 59
This means the 3 consecutive integers are 59, 60, and 61
(You can check by adding them 59 + 60 + 61 = 180)
So the largest angle is 61!
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