summation of external angles of n-gon

The summation of internal angles of n-gon = (n-2)pi.

The summation of external angles of n-gon = Σe(i), where e(i) is an external angle of n-gon, i moves from 1 to n.

Then the below holds.

    Σ(pi-e(i)) = (n-2)pi,

Therefore

    Σe(i) = 2pi.