Originally Posted by
hallsofivy if that is what you are asking about, one way to see that is true is this: Take any point on the inside of the polygon and draw lines from that point to each vertex. That divides the polygon into n triangles. Each triangle has total angle measure 180 degrees so those n triangles have angles adding to 180n degrees. But one angle in each triangle is at that center point and since those angles go all the way around, they add to 360 degrees. So the sum of all the angles at the vertices is, as ebaines said, 180n- 360.
A related formula is that if we have a regular polygon all n angles have the same measure so each angle has measure $\displaystyle \frac{180n- 360}{n}$.