Exterior Angles Investigation

Topic:
Angles

Objective

Your learning objective is to discover the relationship between the exterior angles of a polygon and develop a way to extend your understanding to all regular polygons.

TRIANGLE

1.

What seems to be true about a triangle's exterior angles? Describe what you see.

2.

Suppose the blue angle measures 130 degrees and the pink angle measures 150 degrees. Predict what the measure of the purple angle be?

Note: For the polygons that follow (quadrilateral, pentagon, hexagon), these applets will work best if the polygon is kept CONVEX. If you don't remember what this term means, click here for a refresher.

QUADRILATERAL

3.

What seems to be true about a quadrilateral's exterior angles? Describe what you see.

4.

Suppose the blue angle measures 110 degrees and the pink angle measures 120 degrees and the green angle measures 60 degrees. What will the measure of the purple angle be?

PENTAGON

HEXAGON

5.

What can we conclude about a pentagon's 5 exterior angles? What can we conclude about a hexagon's 6 exterior angles? Describe the phenomena you observed.

Quick Demo. BGM: Andy Meyers

What about regular polygons?

Consider the regular pentagon below. Use the diagram to look at this relationship.

What did you discover about the exterior angles of polygons? Describe how this relates to regular polygons.