Polygon Exterior Angle Sum Conjecture
During this lesson, you will solve statement problems involving Polygon Exterior Angle Sum
Conjecture and its corollary.
VOCABULARY
If you extend one side of a polygon from one endpoint, then you
have constructed an __________________________at the
vertex.
Investigation: Polygon Exterior Angle Sum Conjecture
Alert! All polygons have two sets of exterior angles. Draw one set of exterior angles.
Measure each angle and determine the sum of the entire set. Complete the conjecture
which follows.
Polygon Exterior Angle Sum Conjecture: The sum of the measures of one set of exterior
angles of any n-gon is ________.
Corollary: The measure of one exterior angle of any regular n-gon is ____________.
ALERT! Use this information to complete the final column of your
polygon sum chart!
Sum of Exterior Angles
Measure of Each Exterior
Angle if Regular
(How many sides) does a
regular polygon have
if….each exterior angle
measures __?
Sample Problems
a. What is the sum of the measures of the exterior angles of a decagon?
b. What is the measure of each exterior angle of a regular decagon?
c. (How many sides) does a regular polygon have if the measure of one exterior angle is
36?
Assume that all polygons are regular to complete the chart below:
# Sides
Sum of interior
Angles
Measure of
each exterior
Measure of
each interior
angle
Special Case: Exterior Angle in a Triangle
Final Check: Now, try these problems which follow without any help!
Find the measure of ONE exterior angle of a regular 20-gon.
The sum of the measures of five interior angles of a hexagon is 625. What is the
measure of the sixth angle?