SOLUTION: Give to reasons why minus 2 in the (n-2) x180 equation

Question 936341: Give to reasons why minus 2 in the (n-2) x180 equation
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Assuming you are referring to interior angles in a polygon:

1: You can draw n-2 non-overlapping triangles in an n-gon (you can try small cases such as n = 4, 5, and prove inductively).

2. The sum of all interior and exterior angles is 180n, but the sum of exterior angles is 360 deg, so the sum of interior angles is 180n - 360 = 180(n-2).
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