why do you subtact 2 from n in the formual (n-2)180

Pick an interior point of the polygon. Connect the point to each of the vertices. This gives you n triangles, whose angle sum is 180° * n. You don't have to count the 360° at hte center.

So the sum of the polygon's angles is 180° * n - 360° = 180° * (n - 2).