proof of sum of interior angles of a polygon ?????????

Answer :

From any one point P inside the polygon,

construct lines to the n vertices of polygon , As :



 

There are altogether n triangles.

 Sum of angles of each triangle = 180°  ( From angle sum property of triangle )
 
Please note that there is an angle at a point = 360° around P

containing angles which are not interior angles of the given polygon.

Sum of interior angles of n- sided polygon

= n $\times$ 180°- 360°  = ( n - 2 ) $\times$ 180°  ( Ans )