Name:_________________________________________________________
Period:___________
Date:_____________________
13.3 – Angles of Polygons Notes
Goals: To find the sum of the measures of interior angles in a polygon. To find an interior angle of a polygon. To find the measure of an exterior angle of a
polygon.
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Number of Sides
Sum of Interior Angles
Each Interior Angle (IF
IT IS A REGULAR
POLYGON)
Sum of Exterior
Angles
Each Exterior Angle (IF
IT IS A REGULAR
POLYGON)
Concept #1 – Sum of the Interior Angles
The sum of the measures of the interior
angles of a convex polygon is given by the
formula:
Polygon Vocabulary
Interior Angle:
Regular Polygon –
Exterior Angle:
Find the measure of an interior angle of the
polygon.
Strategy: Interior Angle Sum / Number of Sides
1) Regular Octagon
A) Name the interior angles of the triangle.
2) Regular polygon with 12 sides
Where n = number of sides
Find the sum of the measures of the interior
angles of the polygon.
1) Heptagon
2)
3)
Concept #3 – Finding the Measure of an
Interior Angle of a Regular Polygon
B) Name the exterior angles of the triangle.
Concept #2 – Identifying a Polygon by the
Interior Angle Sum
Concept #5 – Exterior Angles
The exterior angles for any convex polygon
add to __________.
Use the formula:
Example: The measures of the interior angles
of a polygon is 900°. Name the polygon.
1. The measures of the interior angles of a
polygon is 1260°. Name the polygon.
2. The measures of the interior angles of a
polygon is 720°. Name the polygon.
Regular Polygons:
1. Find the measure of an exterior angle of a
regular pentagon.
2. Find the measure of an exterior angle of a
regular octagon.
Irregular Polygons:
Four exterior angles of a convex pentagon have
measures 14°, 87°, 56°, and 30°. Find the
measure of the fifth exterior angle.
Concept #4 – Finding the Measure of an
Interior Angle of an Irregular Polygon
Strategy: Find the interior angle sum and
subtract the given angle measures to find the
missing one.
1)
2)
Name:______________________________________
Use your notes (especially the flow chart!) to answer the following.
Interior Angle Sum Problems
#1-3: Find the sum of the measures of the interior angles of the polygon.
1.
13.3 Polygons Homework Problems
Exterior Angle Problems
1. Find the measure of an exterior angle of a regular hexagon.
4. Name the polygon who has
an interior angle sum of 1080°.
2. Find the measure of an exterior angle of a regular decagon.
3. Find the measures of all the exterior angles in the polygon.
2.
5. Name the polygon that has an
interior angle sum of 1440°.
3.
What do all of the exterior angles add up to?
Nonagon
Finding the Measure of an Interior Angle in a Regular Polygon
Finding the Measure of an Interior Angle in an Irregular Polygon
Find the measure of one interior angle for each regular polygon.
1. Pentagon
2. Hexagon
Find the missing angle measure in the irregular polygons.
1.
2.
3. Heptagon
4. Nonagon
3.