Let S be the internal angle of a polygon and A its external adjacent angle.
Then we have: S + A = 180°
Thus, for a polygon with n sides, we have:
[tex]\sum ^n_{i\mathop=1}S_i+A_i=n\cdot180\degree[/tex]Since the sum of internal angles is given by (n-2)*180°, we have:
[tex]\begin{gathered} (n-2)\cdot180\degree+\sum ^n_{i\mathop{=}1}A_i=n\cdot180\degree \\ \\ \sum ^n_{i\mathop{=}1}A_i=360\degree \end{gathered}[/tex]Therefore, the sum of the exterior angles of a regular polygon is 360°
