The highest exterior angle for a regular polygon is 120 degrees because it relates directly to the number of sides the polygon has.
To understand this, we first need to know how to calculate the exterior angle of a regular polygon. The formula to find the exterior angle (E) of a regular polygon is given by:
E = 360° / n
where n is the number of sides of the polygon. This formula tells us that as the number of sides increases, the size of each exterior angle decreases.
Now, to find out when the exterior angle reaches its maximum value, we need to understand special cases of polygons. The simplest polygon, a triangle (which has 3 sides), has an exterior angle of:
E = 360° / 3 = 120°
When we move to polygons with more sides, like a square (4 sides), the exterior angle is:
E = 360° / 4 = 90°
For a pentagon (5 sides), the angle is:
E = 360° / 5 = 72°
As we keep adding sides, the exterior angles keep getting smaller. In the limit, as the number of sides approaches infinity (in the case of a regular circle), the exterior angle approaches 0 degrees.
Therefore, 120 degrees is indeed the highest exterior angle for any regular polygon, and it only occurs in the simplest polygon type—a triangle. Beyond that, every other regular polygon has an exterior angle less than 120 degrees.