To determine the measure of an exterior angle of a regular 20-gon, we can follow these steps:
1. Understand that the sum of all exterior angles of any polygon is always [tex]\( 360^\circ \)[/tex].
2. In a regular polygon, all exterior angles are equal.
3. If the polygon has [tex]\( n \)[/tex] sides, each exterior angle can be calculated by dividing the total sum of exterior angles by [tex]\( n \)[/tex].
Given that we have a regular 20-gon (a polygon with 20 sides):
[tex]\[ n = 20 \][/tex]
The measure of each exterior angle would thus be:
[tex]\[ \text{Exterior angle} = \frac{360^\circ}{n} \][/tex]
Substitute [tex]\( n \)[/tex] with 20:
[tex]\[ \text{Exterior angle} = \frac{360^\circ}{20} \][/tex]
[tex]\[ \text{Exterior angle} = 18^\circ \][/tex]
Therefore, the measure of an exterior angle of a regular 20-gon is [tex]\( 18^\circ \)[/tex].
The correct answer is [tex]\( 18^\circ \)[/tex].
