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Yesterday I posted this question. The Task was:

Show that there is a greatest number $m$ for which the following statement is true! There is a convex polygon, under whose inner angles exactly $m$ are acute

The solution was, that there is a maximum of $3$.

Now I have asked myself how many acute angles ($m < 90°$) can have a polygon if it is not convex and overlap-free.

Note:
look here, there can be more then $\frac {n}{2}$ such angles, but I don't see an reason why there's a maximum amount of acute interior angles (and there is one)!
Does anyone have an idea?

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    What is a "tip" angle? Does it mean an angle less than a right angle, like the $m$ angles in the earlier question? – 2017-01-05
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    Sorry, I edited it. I mean less then 90° – 2017-01-05
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    "acute angles (m>90°) ": That is the definition of an obtuse angle, not an acute angle. Could you clarify? – 2017-01-05
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    ahhhh, I've mistyped. Now! – 2017-01-05
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    Has noone a idea? :/ – 2017-01-05

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