Why do all exterior angles on a polygon add up to 360 when the interior changes depending on sides?
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Well, that’s not quite true, unless you make 2 important caveats:
– For concave angle, the exterior angle is negative, where you count the angle “backward”.
– The polygon cannot self-intersect.
Imagine you’re walking along the polygon. At each corner, you turn. The amount of turning you made is the exterior angle (negative turning means you turn away from the interior of the polygon). If you walk a full length of the polygon, turning at each corner, then you would have turned a full rotation, which means the total sum is 1 rotation, or 360 degree.
Why you turn a total of 1 round? Well, the number of round you turn is always an integer, because you face the same direction as when you started. And if you turn 0 round total, or at least 2, the polygon must self-intersect, which we don’t allow.
What about interior angle? Sum of interior and exterior is 180 degrees, always. So the total sum of them depends on the number of angles, hence number of sides. But exterior always add up to 360 degree, so the rest is interior.
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