Explore the interior angles of regular polygons by dividing the polygons into triangles.

• Find the central angle measure of a regular polygon
• Relate the sum of the interior angles of a triangle to the sum of the interior angles of a regular polygon
• Apply geometric representations of the expressions (n – 2)180 and 180n – 360 to determine the measure of the interior angles of a regular polygon

• Central angle
• Base angle
• Interior angle
• Isosceles triangle
• Regular polygon

This lesson involves changing the number of sides of a regular polygon. As a result students will observe the consequences of this manipulation on the central angle; infer the relationship between the central angle and the number of sides of a regular polygon; infer the relationship between the base angles of the isosceles triangles and the measure of an interior angle; deduce the geometric and algebraic equivalence of the expressions (n – 2)180 and 180n – 360, which can be used to find the interior angle sum of all regular and irregular convex polygons.