Question

If an exterior angle of a regular polygon is 21.2° how many sides does the polygon have?

Answer 1

`\bf \textit{sum of all exterior angles in a polygon}\\\\ n\theta =360\quad \begin{cases} n=\textit{number of sides}\\ \theta =\textit{angle in degrees}\\ ----------\\ \theta =21.2^o \end{cases}\implies n21.2=360 \\\\\\ n=\cfrac{360}{21.2}\implies n\approx 16.981132\implies n\approx 17`

the reason why the value is not an integer, is most likely because the 21.2° is just an approximation.