There are two regular polygons: one with X sides and one with Y sides with Y>X. Also, coincidentally, the latter has internal angles that are each (Y-X) degrees greater than the former. Also, X+Y is a perfect square.
What are X and Y?
I see that all find the 9:40 solution. I think we can safely ignore the 1--360 which would not be a polygon at all, would it?
Incidentally, when I posted, it was 9:30 am, but the time stamp on my submittal came back as 11:10:49. I could understand a difference by whole hours (different time zones), but see no pattern in this. Where is the home base of Perplexus? How are the date/time stamps derived?