Question

What is the sum of the exterior angles of a regular polygon?Type your answer...

Answer 1

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:

`\sum ^n_(i\mathop=1)S_i+A_i=n\cdot180\degree`

Since the sum of internal angles is given by (n-2)*180°, we have:

`\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}`

Therefore, the sum of the exterior angles of a regular polygon is 360°