Final answer:
A regular polygon cannot have an exterior angle of 21 degrees because its exterior angles must sum up to 360 degrees, and 360 is not divisible by 21 to yield a whole number of sides for the polygon.
Step-by-step explanation:
The reason a regular polygon cannot have an exterior angle of 21 degrees is due to the relationship between the number of sides in a polygon and the measure of its exterior angles. The sum of the exterior angles of any polygon is always 360 degrees. To find the measure of a single exterior angle of a regular polygon, you divide 360 degrees by the number of sides (n). Therefore, the measure of each exterior angle must be a factor of 360 degrees.
For a regular polygon to have an exterior angle of 21 degrees, 360 would have to be divisible by 21, which yields approximately 17.143. Since the number of sides of a polygon must be a whole number, this is not possible, as you cannot have a fraction of a side. Regular polygons must have exterior angles that are divisors of 360, which results in whole number sides.