To answer this question we will set and solve an equation.
Recall that the exterior angle of an n-gon has a measure of:
[tex]\frac{360^{\circ}}{n}.[/tex]
Let n be the number of sides that the polygon that we are looking for has. Since the regular polygon exterior angles with a measure of approximately 17.14 degrees, then:
[tex]\frac{360^{\circ}}{n}\approx17.14^{\circ}.[/tex]
Therefore:
[tex]n\approx\frac{360^{\circ}}{17.14^{\circ}}[/tex]
Simplifying the above result we get:
[tex]n\approx21.[/tex]
Answer: 21 sides.
