Let ABCD be a quadrilateral such that exterior angles formed by extending the sides AD,AB,BC and CD are angles x,y,z and w.
Now, since, sides AD,AB,BC and CD are straight lines, therefore,
⇒∠BAD+x=180∘⇒∠BAD=180∘−x...(i) [Linear Pair].
Adding (i), (ii), (iii) and (iv), we get,
⇒360∘=720∘−(x+y+z+w) [Sum of all the angles of a quadrilateral is 360∘]
Thus, the sum of the four exterior angles is 360∘.
It is well established that regardless of number of exterior angles, the sum of all the exterior angles of a polygon is always 360∘.