Question

Formula of n sided polygon

Answer 1

Answer:

Step-by-step explanation:

You have a polygon of n sides, great.

So you n vertices that make n sides.

Now consider a point P somewhere inside the polygon closer to its centre.

Together with n vertices this point P can make n triangles, right? Right!

The sum of the angles of these n triangles is n×180° because it can be easily shown that the sum of the angles of a triangle is 180° as the straight line forms 180°

Now the above sum n×180° consists of the sum of the angles of the polygon and the sum of the angles formed around point P. The sum the angles around P is obviously 360°.

Therefore it is clear that the sum of angles of an n−sided polygon is n×180°−360°=(n−2)×180°.