Five point star:
Notice there is a pentagon in the centre of the five point star. The exterior angles of this shape must add up to 360°.
If the exterior angles are marked onto a diagram, each one is in a corner of an outer triangle.
Effectively, there are two sets of exterior angles on the central pentagon - depending on the direction in which they are marked: mark these in and each outer triangle will have an angle drawn in two base corners.
There are are five triangles within a five pointed star. The angles in a triangle add up to 180°. 180 x 5 will give the total number of degrees in all the triangles of the star. 900
Earlier, it was said exterior angles on the central pentagon had to equal 360°. Two sets of exterior angles have been marked on the shape. If both of these sets are subtracted (-360 then -360) from the total angles (900), 180 is left. This is the sum of the outer points of the star.
"N" point star:
A star with any number of points will have a central shape (this was a pentagon for the five points star) and the exterior angles of this shape will always add up to 360°.
When calculating for the five point star, 180 was multiplied by 5 (once for each triangle or star point) meaning 5 is n. As the sum of exterior angles does not change, subtracting 360 twice must still be done.
Simplified, the equation is:
(N x 180) - 720