Question 15311
Start with a rectangle for an example, and draw a diagonal.  Notice that you have a 4 sided figure, and there are 2 triangles, each with a sum of 180 degrees for a total of 2*180 = 360 degrees.


Next, draw a pentagon, and from any given vertex, draw the two diagonals from that vertex to the other vertices.  Notice that you have a 5 sided figure, with two diagonals.  There are 3 triangles, each with sum of 180 degrees for a total of 3*180 = 540 degrees.



Next, draw a hexagon, and from any given vertex, draw the three diagonals from that vertex to the other vertices.  Notice that you have a 6 sided figure, with three diagonals.  There are 4 triangles, each with sum of 180 degrees for a total of 4*180 = 720 degrees.


Now, notice the pattern.  If there are n sides, there will be two less triangles than sides, which is n-2 triangles, and the sum of the angles will be (n-2)* 180 degrees.


The formula for the sum of the angles of a polygon with n sides is 180(n-2).


R^2 at SCC