Geometry: Sum of Exterior Angles of Polygons

Objectives

• Determine that the interior angle of a polygon and an exterior angle of a polygon form a linear pair (i.e., the 2 angles are supplementary)
• Determine that if one exterior angle is drawn at each vertex of a convex polygon, then the sum of the measures of those exterior angles is 360°
• Determine a formula for the measure of one exterior angle of a regular polygon and use this to discover an alternative form for the formula that is typically used to calculate the measure of the interior angle of a regular polygon

Vocabulary

• exterior angle of a polygon
• regular polygon
• irregular polygon
• interior angle of a polygon

About the Lesson

This lesson involves moving an arrow along the side of regular and irregular polygons to form an exterior angle with the adjacent side of the polygon. As a result, students will:

• Discover that an interior and exterior angle of a polygon form a linear pair.
• Determine that the sum of the measures of the exterior angles of any convex polygon is 360°.