For a given polygon with n sides, the formula for the exterior angles is
[tex]\begin{gathered} \frac{360}{n}=\theta \\ \text{where }\theta\text{ is an exterior angle. } \end{gathered}[/tex]
In our case,
[tex]\theta=17.14[/tex]
then, by substituting this value into our formula,we get
[tex]\frac{360}{n}=17.14[/tex]
By moving n to the right hand side, we have
[tex]360=17.14\times n[/tex]
and n is given as
[tex]\begin{gathered} n=\frac{360}{17.14} \\ n=21.0035 \end{gathered}[/tex]
Therefore, by rounding down this result, the answer is 21 sides.
