Final answer:
A regular polygon can't have an exterior angle of 360 degrees since the sum of all exterior angles in any polygon is 360 degrees, making the scenario described impossible.
Step-by-step explanation:
To find the number of sides of a regular polygon where each exterior angle has a measure, we must first understand the relationship between exterior angles and the total degrees in a polygon. The sum of the exterior angles of any polygon is always 360 degrees. Therefore, if one exterior angle has a measure of 360 degrees, it would indicate that the polygon is not feasible because regular polygons must have multiple sides with the exterior angles adding up to 360 degrees.
It is not possible for a regular polygon to have an exterior angle that is equal to the total sum of all exterior angles. In geometric terms, each exterior angle of a regular polygon can be found by dividing 360 degrees by the number of sides, n. Since one cannot divide 360 degrees by 360 and get a whole number, this suggests that the question might have a typo or there's a misunderstanding. Typically, regular polygons have exterior angles that are less than 180 degrees.