A regular polygon with one exterior angle measuring 1 degree would have 360 sides. To understand why, let’s delve into the concept of exterior angles.
The sum of all exterior angles of any polygon is always 360 degrees, regardless of the number of sides it has. Since a regular polygon has equal exterior angles, you can find the number of sides by dividing the total exterior angle sum by the measure of one exterior angle. So, in this case, we have:
Number of sides = Total exterior angle sum / One exterior angle
Substituting in the values:
Number of sides = 360 degrees / 1 degree = 360
This means that if each exterior angle is 1 degree, the polygon must have 360 sides.