Question

A formula for calculating the size 0 of the interior angle of an 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° .