I was solving problems from Paul Zeitz's book "The Art and Craft of Problem Solving." There is a problem which states
3.2.11 Fix the proof in Example 2.3.5 on page 45. Show that even a concave polygon has an acute angle that we can use to "snip off' a triangle. Why do we need the extreme principle for this?
Example 2.3.5 he speaks of is to prove that sum of angles in a polygon is 180(n-2) degrees.
I believe he meant an angle less than 180 degrees and not an acute angle since I can think of cases where a concave polygon has no acute angles.
Please give me a hint as to how I can use the extreme principle in order to figure out an angle that is < 180 degrees (instead of acute) among all the internal angles of a polygon. I cannot use the fact that the sum of internal angles of any polygon = 180(n-2), n being number of sides in the polygon. That is because the intention is to prove that the sum is 180(n-2) using the fact that one of the angles is less than 180 degrees so it would end up in a circular logic.