Exterior+Angles+of+a+Polygon+
Exterior Angles of a Polygon
Exterior angle is formed when you extend one side of a polygon from one
endpoint. There is an exterior angle at each vertex of a polygon.
Regular polygon - a polygon that has congruent angles and congruent
sides.
Let's explore exterior angles of polygons...
Tools needed: Straightedge, calculator, paper, pencil, and protractor
Construct the following 5 shapes on 5 separate sheets of paper. Be sure to leave room around each shape to
extend sides: Triangle, Quadrilateral, Hexagon, Pentagon, Heptagon
Step 1: With the protractor, measure all the interior angles for each of the shapes. Confirm that the sum is
correct by using the Sum of interior Angles formula from the previous exploration in this module.
Step 2: Extend each side in one direction to form an exterior angle as illustrated in the diagram above.
Step 3: Using Linear Pair angles are Supplementary, determine the measure of each exterior angle of the
polygon
Step 4: Calculate the sum of the measures of the exterior angles and enter the data in the chart below.
Number of sides 3 4 5 6 7
Sum of the measures
of the exterior angles
Your Assignment:
Create a presentation to submit in the dropbox that contains the table above, pictures of your exploration, a
conjecture about the sum of the exterior angles of a polygon as well as answers to the questions below.
1. What conclusion can you make with your observed calculations?
2. What if the number of sides is n? What would be the sum of the measures of the exterior angles?
3. Suppose you are given a regular hexagon named ABCDEF. What would be the measure of each of
the exterior angles of this regular hexagon?