This inquiry-based activity introduces students to Interior Angle Sum Theorem for convex polygons. The two-page worksheet guides them to find patterns in the angle sums. Then, they divide each polygon into triangles to discover why each sum is a multiple of 180 degrees. They extend this pattern to a 100-sided polygon and then develop a formula for a polygon with n sides. The last part of this activity extends the formula to regular polygons and students find the measure of one angle. This activity can be done individually or with partners. Two versions are included: one in which students measure the angles with a protractor to complete the chart, and one with the chart already completed so they can just start off by analyzing the patterns.
For another great inquiry-based discovery activity, try:
Exterior Angles Inquiry Activity
For more great math resources, try:
Adding Integers Inquiry Activity
Discovering Laws of Exponents: Inquiry Activity
Learning Stations: Discovering Polyhedra