Maximum number of acute interior angles in a hexagon.

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Is it possible for a hexagon (in the plane, non-convex, non-overlapping) to have $5$ acute interior angles? It's possible for a pentagon or a hexagon to have $4$ acute interior angles. There are related questions on this site, but they are for general $n$-gons and no one seems to have a definitive answer. So what about just 6-gons?

Want to know what I tried? Fine, I wore out 3 Expo markers on my whiteboard trying stuff.

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1 Answer

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Yes, it is possible to have $5$; see this figure for an example. You can easily formalize the argument once you see it; I have left that as an exercise.

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