Section 8.1 Find Angle Measures in Polygons
Definitions:
1. Polygon 2. Vertex 3. Convex 4. Non-convex (
)-
5. Equilateral 6. Equiangular 7. Regular 8. Diagonal -
Identify each polygon by the number of sides, n.
# of
Sides
Name
3
4
5
6
7
8
9
10
12
n
n-gon
Measure of exterior
angle of regular
polygon
Measure of one
interior angle of
regular polygon
Measure of all
interior angles of
regular polygon
Determine if the figure is a polygon. If the figure is a polygon, classify it as convex or
nonconvex.
1.
2.
3.
4.
5.
6.
7.
8.
Use the diagram at the right to answer the following questions.
9. Name the polygon by the number of sides it has.
B
A
C
10. Name all of the diagonals that have vertex E as an endpoint.
G
D
11. Name the consecutive angles to A.
Draw a figure that fits the description.
12. A convex octagon
13. An equilateral quadrilateral that is not equiangular
14. An equiangular quadrilateral that is not equilateral
F
E
1. We can divide a polygon into triangles by drawing the diagonals from 1 vertex.
Ex.
 Draw the diagonals from vertex A of
pentagon ABCDE.
 How many s did you form?____



Draw the diagonals from vertex T in the
hexagon PQRSTU.
How many s did you form?____
Compare the # of sides in the polygon
with the # of s formed. There are 2
fewer s than sides!!
B
A
C
E
D
P
Q
R
U
T
S
Therefore, the sum of all of the (interior) angles of a n-gon is (n - 2)180
LEARN!
The sum of the angles of a pentagon is _______  180 = __________
The sum of the angles of a hexagon is ________  180 = __________
2.
Polygon Exterior Angles Theorem: The sum of the measures of the exterior
angles of a convex polygon, only one exterior angle at each vertex, is 360.
T



Draw the following rays. GE , EO, OM , MT , TG
What is the sum of these 5 exterior s?_______
If this pentagon is regular, then each of
the 5 exterior angles would be _______.
Show arithmetic.
G
M
E
O
3.
(Theorem) The measure of each exterior angle of a regular polygon equals
A
Ex. 1
 BCDEFG is a regular
__________.
 ABG is an _____________
angle.
 mABG = ________.
B
360
.
n
C
G
D
F
E
Ex.2
What’s the measure of each exterior angle of a regular
a.) decagon
c.) nonagon
b.) dodecagon
d.) triangle
Ex.3
If the exterior angle of a regular hexagon is 60, then the interior angle = _______.
Explain:
4.
To find the measure of each interior angle of a regular convex polygon,
360
, n = # of sides, then, subtract from 180.
1st find each exterior  by
n
Ex. 1
Find the measure of each exterior angle and interior angle of a regular:
a.) octagon
b.) pentagon
c.) 7-gon