Activity 5.1: Exterior Angles - Drill #1
Solve for the exterior angle of each polygon on the figure.
1. Exploring Relationships Between Interior and Exterior Angles
In the polygons presented, what relationship do you observe between the interior and exterior angles at each vertex? Can you explain why this relationship holds for all polygons, regardless of the number of sides?
2. Exploring the Relationship Between Exterior and Interior Angles in Triangles
2.A. Look at the triangles shown in the applet and focus on any of the triangle’s exterior angles. Can you describe how this exterior angle is related to the two non-adjacent (or remote) interior angles of the triangle? Use specific angle measures from the triangles to support your explanation.
2.B. Make a general statement relating an exterior angle of a triangle to the interior angles remote to that exterior angle. Justify your statement.
3. Predicting the Exterior Angle Measurement
Before using the applet to find the exterior angle, predict the measure of the exterior angle of a vertex in a regular polygon (like a triangle or a square). Explain your reasoning. After predicting, use the applet to check your prediction. Was your reasoning correct? Why or why not?
4. Generalizing Angle Sum Rules
Using the applet, calculate the sum of the interior angles for the given quadrilateral and pentagon. Based on your calculations, derive a general formula to calculate the sum of the interior angles for any polygon with 'n' sides. How does this formula relate to the exterior angle measures?