If a polygon is convex, climate the amount of the steps of the exterior angles, one at every vertex, is 360 ° . think about the amount of the actions of the exterior angle for an n -gon.

The sum of the steps of the exterior angles is the difference in between the sum of steps of the linear pairs and the sum of steps of the inner angles.

that is, the sum of the exterior angles n is

N = 180 n − 180 ( n − 2 )

distribute 180 .

N = 180 n − 180 n + 360             = 360


Example:

*

m ∠ 1 + m ∠ 2 + m ∠ 3 + m ∠ 4 + m ∠ 5 = 360 °


(In the instance of a non-convex polygon, you might need to think about some that the exterior angles as negative values.)


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