Why do you subtract 2 from n to find the sum of interior angles?

Answer 1

This has to do with the way in which the sum of the angles is derived.

First you select a point inside the polygon and then join that point to each of the vertices. For a polygon with n sides, this gives rise to n triangles.

The sum of the 3 angles of any triangle is 180 degrees. So the sum of the angles of all the triangles is n*180 degrees.

Now, the "outer" angles of these triangles correspond to the interior angles of the polygon. But the sum also includes the angles formed arounf the central point. The sum of all the angles around this central point is 360 degrees. This is not part of the sum of the interior angles of the polygon and so must be subtracted.

Thus, the interior angles of a polygon sum to n*180 - 360 degrees or 180*(n- 2) degrees.