In a convex n-gon, the sum of n - 1 internal angles is 1485 degrees. What is n?
The total number of degrees in all the interior angles of an n-gon is (n - 2)180o.
10 sides would be too few because they would create (10 - 2)180o = 1440o; but this is close.
11 sides create (11 - 2)180o = 1620o. Subtracting 1485o from this number gives 135o;
so if 10 of the angles give a total of 1485o and the 11th angle has 135o, we would get an 11-sided polygon.