The measure of an exterior angle of a regular nonagon, which is a nine-sided polygon, can be calculated using the formula for exterior angles of any regular polygon. Specifically, the formula for the measure of one exterior angle is:
Exterior Angle = 360° / n
Where n represents the number of sides of the polygon. For a nonagon, n = 9.
Substituting 9 into the formula gives us:
Exterior Angle = 360° / 9
Calculating this, we find that:
Exterior Angle = 40°
Thus, each exterior angle of a regular nonagon measures 40 degrees.
This means that if you were to extend any one side of the nonagon, the angle formed between that extended line and the adjacent side would be 40 degrees. Understanding exterior angles is not only essential in geometry but also plays a significant role in various applications such as architecture, engineering, and even aesthetics in design.