The sum of the interior angles of a polygon of n-sides is



Since the polygons are regular, all the interior angles are the same,
so each one is that expression divided by n



That must be equal to a whole number, say, W. Since n does not divide
evenly into n-2, it must divide evenly into 180°. So we go through
the list to see which numbers divide evenly into 180°:

Polygon a. Convex 15-gon, yes, since 15 divides evenly into 180°.
Polygon b. Convex 16-gon, no
Polygon c. Convex 17-gon, no
Polygon d. Convex 18-gon, yes, since 18 divides evenly into 180°.
Polygon e. Convex 19-gon, no
Polygon f. Convex 43-gon, no
Polygon g. Convex 44-gon, no
Polygon h. Convex 45-gon, yes, since 45 divides evenly into 180°.
Polygon i. Convex 46-gon, no
Polygon j. Convex 47-gon, no

So the value of the interior angles approaches 180° as the number 
of sides of the polygon increases.

The sum of the exterior angles of any polygon is 360°.  So
each one of a regular polygon is 

So the value of the exterior angles approaches 0° as the number 
of sides of the polygon increases.

Edwin