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Name:
Period:
Geometry
6.1
Polygon Angle-Sum Theorems
Notes
Vocabulary
Equilateral Polygon: Polygon with all
congruent ______________________.
Equiangular Polygon: Polygon with all
congruent _______________________.
Regular Polygon: Polygon that is both
_______________________ and
______________________.
Total degrees of INTERIOR Angles of Polygons
Recall: The total degrees of the angles of a triangle is _________________.
From one vertex, connect to all other vertices to make as many triangles as possible.
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
# of triangles
within shape
Total
degrees in
the figure
 To find the total degrees, take the number of triangles the shape can be split into
and multiply it by ______________________.
 To find the total degrees for any polygon with n sides, use the formula:
IF the polygon is equiangular (which also applies to regular), then the interior angles are
all congruent. So, to find EACH interior angle, use the following formula:
RECALL:
What are the total degrees of a triangle?
If the triangle is equiangular, what is the measure of EACH angle?
Example:
What are the total degrees of an octagon?
If the octagon is regular (all congruent angles), what is the measure of EACH angle?
1.) How many total
degrees are in an octagon?
Practice Problems:
2.) How many total
3.) Which polygon has a
degrees are in a dodecagon? total of 1260 degrees?
4.) What is the measure of
each interior angle of a
regular hexagon?
5.) What is the measure of
each interior angles of an
equiangular undecagon?
6.) A regular polygon’s
interior angles add to 900
degrees. What is the
measure of each interior
angle?
Total degrees of EXTERIOR Angles of Polygons
Recall: An EXTERIOR ANGLE is formed by
extending one side of a polygon.
For each of the following polygons:
Create one exterior angle at each vertex using a straightedge.
 Then use a protractor to measure each exterior angle.
 Last, add the measures of the exterior angles for each figure.

Sum of three exterior angles:
Sum of four exterior angles:
Sum of five exterior angles:
Sum of six exterior angles:
So the SUM OF EXTERIOR angles of a polygon (regardless of the number of sides) is
1.) What is the sum of
exterior angles of a
nonagon?
_______________________________.
Practice Problems:
2.) What is the sum of
3.) What is the measure of
exterior angles of a 15-gon? EACH exterior angle of a
regular hexagon?
SUMMARY
Interior Angles Exterior Angles
Sum
Each
More Practice
1.) Find the sum of the measures of the
interior angles of the figure.
2.) Find x and y.
3.) Find the measure of an interior angle
and an exterior angle of a regular polygon
with 16 sides.
4.) If one interior angle of an equiangular
n-gon is 162 degrees, how many sides does
the n-gon have?