Quiz

Ah, here. The second option simply doesn't allow for an odd-sided polygon. With an odd-sided polygon, the beginning and end of the sequence of segments are guaranteed to be on the same side of the line. An odd number of angles equals an odd number of sides, which equals an even number of intersecting segments (not counting the closing segment). The beginning and end are on the same side.
If the problem is expanded to an even-sided polygon, then yes, the second option would need to be proven (but that shouldn't be too difficult either).