Why does the formula (n-2) * 180 give you the sum of the interior angles of a convex polygon?
The formula we use to find the sum of the interior angles of any polygon comes from the following idea: Suppose you start with a pentagon. If you pick any vertex (the point where any 2 sides meet) of that figure, and connect it to all the other vertices, how many triangles can you form? If you start with a vertex (which is already connected to two adjacent vertices) and connect it to all other vertices you form three triangles. Each triangle contains 180 degrees. So the total number of degrees in the interior angles of a pentagon is: 3 * 180 deg = 540 deg Using the pentagon example, we can come up with a formula that works for all polygons. Notice that a pentagon has 5 sides, and that you can form 3 triangles by connecting the vertices. That’s 2 less than the number of sides. It’s the same principle for all polygons. If we represent the number of sides of a polygon as n, then the number of triangles you can form is (n-2). Since each triangle contains 180 degrees, that gives us the form
