Every (convex) star polygon with n vertices can be associated with a permutation on {1,2, . . . , n } . It is known that the sum of interior angles of the polygon is solely determined by £». In this thesis, we give an exact formula to calculate the sum of interior angles in term of £». We make use of this formula to derive a recurrence relation concerning the number of star polygons having a particular value of sums of interior angles.