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Section 3-5
Angles of a
Polygon
Polygon
• Means: “many-angled”
• A polygon is a closed figure formed by a
finite number of coplanar segments
a. Each side intersects exactly two other
sides, one at each endpoint.
b. No two segments with a common
endpoint are collinear
Examples of polygons:
Ex #1
Ex#2
Two Types of Polygons:
1. Convex: If a line was extended from the
sides of a polygon, it will NOT go through
the interior of the polygon.
Ex #1
2. Nonconvex: If a line was extended from
the sides of a polygon, it WILL go
through the interior of the polygon.
Ex#2
Polygons are classified according
to the number of sides they have.
*Must have at least 3
sides to form a
polygon.
Special names
for Polygons
*n stands for number of sides.
Number of
Sides
Name
3
4
5
Triangle
Quadrilateral
Pentagon
6
7
8
Hexagon
Heptagon
Octagon
9
10
n
Nonagon
Decagon
n-gon
Diagonal
• A segment joining two
nonconsecutive vertices
*The diagonals
are indicated with
dashed lines.
Definition of Regular
Polygon:
• a convex polygon with all sides
congruent and all angles
congruent.
Interior Angle Sum Theorem
• The sum of the measures of
the interior angles of a convex
polygon with n sides is
S = 180 (n - 2)
One can find the measure
of each interior angle of a
regular polygon:
1. Find the Sum of the
interior angles S = 180 (n - 2)
2.Divide the sum by the
S
number of sides the
regular polygon has.
n
One can find the number of sides a
polygon has if given the measure of
an interior angle
180n  2 
n
Exterior Angle Sum Theorem
• The sum of the measures of
the exterior angles of any
convex polygon, one angle at
each vertex, is 360.
One can find the measure of each
exterior angle of a regular polygon:
360
= exterior angle
n
or
One can find the number of sides a polygon
has if given the measure of an exterior angle
360
=n
exterior angle