Triangulation Exploration

OK Math Cadets, we’re going to derive our own formula.  First, let’s extend this pattern. How many triangles can you break a pentagon into? What about a Hexagon? Complete the following table and see if you can find a relationship between the number of sides and the number of triangles.  Need a hint? Click the “Hint” button below.

Alright, we’re almost ready to create our own formula.  As we have seen, every time we add a side, we add 180 degrees to the interior angle sum.  Unfortunately, we can’t just multiply 180 by the number of sides. If we did, a triangle’s angles would add to 540 degrees, instead of 180.  Let “n” be the number of sides in a polygon.  Can you figure our a formula using “n” for the sum of the interior angles?

What if we want to know the measure of one specific angle in a regular polygon?  How can we modify our formula to find the measure of an interior angle in a regular polygon?  Remember, in a regular polygon each interior angle is equal.