To solve this problem, we need to apply the concept that the sum of the exterior angles of any polygon is always 360 degrees. This is a property that holds true for all polygons, regular or irregular. For a regular polygon, all of the exterior angles are equal.
Given that one exterior angle measures 18°, we can find the number of sides of the polygon by using the following steps:
1. Take the sum of the exterior angles for any polygon, which is 360°.
2. Divide this sum by the measure of one exterior angle to determine how many such angles (and therefore sides) the polygon has.
So, we do this calculation:
Number of sides = 360° / measure of one exterior angle
Now, substitute the given measure of one exterior angle (18°):
Number of sides = 360° / 18°
When we divide 360 by 18, we get:
Number of sides = 20
So, the polygon with an exterior angle of 18° has 20 sides.
