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put this solution on YOUR website!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).
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