Sum of Interior and Exterior Angles of Polygons

Use the Geogebra applet below to explore the relationship between the number of sides of a polygon and the interior and exterior angles of that polygon. You can move the points in the polygons, but be sure to keep the polygon convex!

Discovery Activity 6.1

Fill in the spreadsheet on the right with the number of sides of the polygon and the corresponding sums of the interior and exterior angles. Have your partner fill in the chart on your worksheet. Click the checkboxes next to the drawing to make the interior or exterior angles visible. Questions to answer on your worksheet: 1) As you increase the number of sides of the polygon, how does the sum of the interior angles change? 2) Click on the Triangles checkbox and notice how the polygons can be broken down into triangles. How does the number of triangles relate to the sum of the interior angles? 3) Use your observations to write a formula that could be used to calculate the sum of the interior angles of a polygon given the number of sides, n. 4) If the polygon were regular, how would you find the measure of just one interior angle? 5) What do you notice about the sum of the exterior angles? 6) How would you find the measure of one exterior angle if the polygon were regular?