Education Technology

# Activities

• ##### Subject Area

• Math: Geometry: Quadrilaterals and Polygons

9-12

45 Minutes

• ##### Device
• TI-Nspire™
• TI-Nspire™ CAS
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• TI-Nspire™ Apps for iPad®
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.6

## Interior Angles of Regular Polygons

#### Activity Overview

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

#### Objectives

• 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

#### Vocabulary

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

#### About the Lesson

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.