One of the properties of polygon is that the sum of all exterior angles is 360.
How can this be true? For example in a polygon with six sides I get the following exterior angles: 270, 175, 260, 238, 217, 235 degrees.
The angle sum of a polygon of n sides is actually $\displaystyle \begin{align*} (n-2)\,180^{\circ} \end{align*}$. The only way your angle sum can be $\displaystyle \begin{align*} 360^{\circ} \end{align*}$ is if your polygon is a quadrilateral.