The maximum is n-3 reflex angles

First, there are three facts that must be established:
1. a reflex angle is an angle measuring between 180 and 360 degrees
2. the number of degrees total in a polygon is 180(n-2)
3. a polygon may have any angle configuration that adds up to the required number of degrees

Let's assume a reflex angle 180+x, where x is as small a positive number as necessary. 180(n-2) divided by 180+x would equal n-3 with a remainder of fewer than 180 degrees to be distributed among the three other angles.