Sum of Interior Angles of a Polygon
Determine a formula for finding the sum of the interior angles of a polygon. Look up the definition of a diagonal of a polygon. Use this definition to create the diagonals of the polygons below. Determine how many triangles each polygon can be divided into. Use what you know about the sum of the interior angles of a triangle to find the sum of the interior angles of each polygon. Create the interior angle measures for each polygon. Compare the sum of the interior angles for each polygon to your solutions. Where your correct? Explain why or why not.
Write a formula using n for number of sides of the polygon and d for sum of the interior angles of the polygon. Test your formula: Decide a number of sides n of a polygon ( n > 8). Using your formula, determine the sum of the interior angles of this polygon. Open GeoGebra in Chrome. Create a polygon of your own with the number of sides you chose above. Create the interior angle measures for your polygon. Does the sum of these interior angles equal the solution you found using your formula? If not, why not? If so, does this prove your formula is correct? Discuss your findings with a classmate.