Introducing Angle Sum Property Of A Polygon

Since ages, we have been introducing angle sum property of a polygon in the following way…

Suppose we need to find angle sum of a pentagon

Here we have a pentagon ABCDE.

In order to find the angle sum, we draw diagonals from one of the vertices of the pentagon and divide it into triangles.

and hence generalize

Angle sum of any Polygon = (n – 2)×180 degrees , where n represents the number of sides .

But I find the following method quite interesting.

We can generalize this for an n-sided polygon as

From student’s point of view, connecting to the center is more easier than drawing diagonals as the number of sides increases.