Interior & Exterior Angles in Scratch

Use Scratch to make the following regular figures: square, triangle, pentagon, hexagon, heptagon. Complete the table below as you go.

# Sides

Rotation in  Scratch

Sum of Interior Angles

Sum of Exterior Angles

3

4

5

6

7

What patterns do you see in the table?

What do you notice about the sum of the exterior angles of a polygon?

What is the sum of exterior angles on a 43-sided figure?

Find an equation that relates the number of sides to the sum of the interior angles.

Graph the Sum of Interior Angles vs. Number of Sides.

Describe the graph in detail.

Use your equation to determine the sum of the interior angles of a 43-sided figure.

If the sum of the interior angles of a polygon is 2340°, how many sides does it have?

Create a graph in Desmos to show the relationship between the sum of the interior angles and the number of sides.

Use Desmos to determine the equation of the line of best fit.

How does the equation given by Desmos compare to the equation you found? Are they equivalent? If so, show that they are algebraically.

What conclusions can you make about how the sum of the interior angles of a polygon are related to the number of sides?