# Activities

• • • ##### Subject Area

• Math: Geometry: Quadrilaterals and Polygons
• Math: Geometry: Triangles

• ##### Author 9-12

42 Minutes

• ##### Device
• TI-Nspire™
• TI-Nspire™ CAS

2.0

• ##### Other Materials
student answer sheet and steps for the students to follow along with

## The sum of the interior angles of regular polygons

#### Activity Overview

The students will construct triangles within regular-sided polygons to determine the sum of the interior angles. They will then, using statistics, create a linear regression to determine the relationship between the number of sides of a regular polygon and the sum of its interior angles.

#### Before the Activity

Send the activity to each handheld. The only prior knowledge the students should know is the sum of the interior angles of a triangle.

#### During the Activity

Make sure the students know how to use the TI-Nspire. They need to be able to construct segments and make calculations.

#### After the Activity

Extensions include:

• Calculating the measure of one interior angle of an n-sided regular polygon.
• Calculating the sum of the exterior angles of an n-sided regular polygon.
• Calculating the measure of one exterior angle of an n-sided regular polygon.