In the lesson 1.03 Project Development, you looked at several polygons to come up with a pattern for the sum of the angles measures of the polygon as the number of sides increased. This processes is called Inductive Reasoning. Inductive reasoning is the process of observing, finding a pattern, making a conjecture (guess) about that pattern, and then testing that conjecture. We use Inductive Reasoning to learn almost everything we know - from opening a door to how to use a fork. Nobody taught us how to do those things. We simply observe, conjecture, test, and repeat until we figure it out. In this Project Development, you will refine your conjecture more.

Directions

Use the table you created in lesson 1.03 and the pattern you described to come up with a formula that gives you the sum of the angles measures of a polygon if you know the number of sides. Your formula should have only one variable (the number of sides of the polygon) and should give you the angle measure sum when you put a number in for the variable and do the resulting calculation.

Test your formula

Test your formula for several values using the table you created in lesson 1.03. For example, when you input 5 into your formula, you shoud get 540.

Mark a table

Complete the following table for polygons using the formula you created.

Number of sides 10 12 15 20 100
Sum of Angle Measures 1440o
Search the internet

Search the internet for a formula for the sum of the interior angles of a polygon, and compare your formula to what you find.
Resond to the following questions below. Include both your formula and the formula you found on the internect in your response.

What is the same about the formulas? What is different? Do they both work? If they both work and are different, why can both of them work?