If a polygon has 42 sides, what should the sum of all the deflection angles be?
I know what a deflection angle is, but I have no clue how to answer this question with the information I've been provided.
2026-03-30 08:55:14.1774860914
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Sum of all deflection angles.
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A kind of cool (but not particularly rigorous) way to see this is to picture the polygon in the plane and then "zoom out." As you do, all the lines constituting the exterior angles converge to a point and the sum is then evidently 360. You can make this rigorous if you really want to...but I'll leave it as is.
Consider a $3$-gon. What is the sum of its deflections angles? What about a $4$-gon? $5$-gon? $\ldots$