In their investigations, students realized that they could take the number of sides on a polygon, subtract it by 3, and arrive at the number of diagonals [s-3 = d]. Continuing this line of thought, students extended the process to identify the relationship between diagonals and triangles within a polygon. If students added 1 to the number of diagonals in a polygon, they then could determine the total number of triangles within the polygon [d + 1 = t]. Putting it all together, students discovered that subtracting 2 from the number of sides on a polygon and multiplying the difference by 180 gives the sum of interior angles. [(n-2)180, where n = number of sides of the polygon].
Although this process seemed challenging at first, students were able to see the existence of patterns. Once the patterns were analyzed and discussed, students were able to generate their own algebraic equations to describe the relationships.