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Polygons & Their Angles: the Basics (page 1)
1. A polygon is a closed plane figure bounded by 3 or more straight sides.
2. Each corner point where 2 sides meet is called a vertex. A polygon has as
many vertices as it has sides.
3. Special cases of polygons:
• An equilateral polygon has all sides congruent.
• An equiangular polygon has all angles congruent.
• A regular polygon is both equilateral and equiangular.
- Examples of a polygon and non-polygons:
B
A
G
F
L
vertex
side
E
M
K
J
C
H
N
O
I
D
Not a polygon; figure is
open, not closed.
A 5-sided
polygon:
a pentagon.
Not a polygon; two
sides intersect
between vertices.
Not a polygon;
no straight
sides.
4. Polygons can be convex or concave.
Q
R
P
S
U
T
V
A
B
diagonal
W
X
Y
Convex: has no diagonal which
passes outside the polygon. (A
diagonal is a line between any two
non-adjacent vertices.)
Concave: has at least 1 diagonal
which passes outside the polygon.
Z
5. Polygons have interior angles.
Interior angles are formed by two
adjacent sides, inside the polygon.
interior
angles
interior
angles
6. Interior Angles Sum Formula:
The sum of the interior angles of an n-gon (a polygon with n sides) is
Sum = (n-2)•180°
Example: What is the sum of the interior angles of a 15-gon?
Answer: For n = 15, (n-2)•180° = (15-2)•180° = 13•180° = 2,340°
Polygons & Their Angles: the Basics (page 2)
7. Polygons have exterior angles.
Exterior angles are formed by a
side and an extension of an
adjacent side.
1
2
5
3
4
8. Exterior Angles Sum Theorem
The sum of the exterior angles of any polygon is always 360°.
Example 1: What is the sum of the exterior angles of a 21-gon?
Answer: 360°, by the Exterior Angles Sum Theorem.
Example 2: What is the measure of each exterior angle of a regular 21-gon?
Answer: 360°/21 = 17.14°
dwa 4/07/13