now, recall that the sum of all interior angles is 180(n-2), now, let's say one angle is θ, and there are "n" sides in the polygon, so if add up all the θ angles, what the sum will then be is just θn, or that product, therefore,
[tex]\bf \theta n=180(n-2)\quad
\begin{cases}
\theta =angle~in\\
\qquad degrees\\
n=number~of\\
\qquad sides\\
-------\\
\theta =108
\end{cases}\implies 108n=180n-360
\\\\\\
360=72n\implies \cfrac{360}{72}=n[/tex]
and surely you know how much that is.
