A convex polygon is one that has no reentrant corners, or to put it differently, has no interior angles greater than . Figure 1 below is convex; Figure 2 is not.
An acute angle is one that is less than a tight angle, that is, less than .
Prove that a convex polygon with sides can never have more than acute angles and that for any it is possible to construct a polygon with exactly acute angles.
For the proof, see the Comments.