Posted by emily on Monday, April 19, 2010 at 6:19pm.
If it has n sides you make n right turns to get all the way around the outside and end up going the same direction you were going at the start.
So each right turn is 360/n
Each interior angle is the supplement of that right turn
180 - (360/n)
so each interior angle = (180 n -360)/n
each = 180 (n-2)/n
the sum is then 180(n-2)
check that
triangle 180 (3-2)= 180 sure enough 180
square 180(4-2) = 360 yes
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