Which of the following best describes the use of the formula s=(n-2)180 where n is the number of sides

Okay, so we know the sum of the interior angles of a triangle is 180 degrees. (Consider triangle ABC with a line parallel to the base (AB) and touching angle C, then AC or BC are transversals and angles A+B+C = 180. We see this because alternate interior angles are equal to a transversal and angle A+B+C do a complete rotation from one side of the straight line to the other or 180 degrees.

Now consider the pentagon ABCDE, 

Start with vertex A and connect it to all other vertices (it is already connected to B and E by the sides of the pentagon). Three triangles are formed. The sum of the angles in each triangle contains 180 degrees. The total number of degrees in all three triangles will be 3 times 180 or 540 degrees.
Note that the Pentagon has 5 sides and 3 triangles were formed by connecting the vertices. The number of triangles formed by connecting the vertices of a polygon will always be 2 less than the number of sides, n. Therefore we have,
sum of interior angles of a polygon is (n-2)*180 where n is the number of sides.


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