Download Polygon Exterior Angle Sum Theorem

Polygon Exterior Angle Sum
Theorem
During this lesson, you will solve
statement problems involving Polygon
Exterior Angle Sum Theorem and
its corollary.
Mrs. McConaughy
Geometry
1
Vocabulary
If you extend
one side of a polygon
I
from one endpoint,
then you have
n
t an ____________at
exterior angle
constructed
the
e
vertex. r
i
o
r
Exterior angle
Mrs. McConaughy
Geometry
2
Investigation:
Polygon
Exterior
Alert!
Each student has
been given
a
different pair
of polygons.
Angle
Sum Theorem
Alert! All polygons have two sets of exterior angles. Draw one
set of exterior angles. Measure each angle, then determine
the sum of the entire set. Complete the theorem which
follows.
Mrs. McConaughy
Geometry
3
The sum of the
measures of one set
of exterior angles of
a convex polygon is
360°.
1
3
2

m1  m2  m3  360
Mrs. McConaughy
Geometry
4
The sum of the
measures of one set
of exterior angles of
a convex polygon is
360°.
1
2
4
3

m1  m2  m3  m4  360
Mrs. McConaughy
Geometry
5
The sum of the
measures of one set
of exterior angles of
a convex polygon is
360°.
2
1
3
5
4

m1  m2  m3  m4  m5  360
Mrs. McConaughy
Geometry
6
one exterior
The measure of each
angle of a regular (equiangular, or
equilateral) polygon is
360
n
Mrs. McConaughy
Geometry
7
Polygon Exterior Angle Sum
Theorem
Polygon Exterior Angle Sum
Theorem: The sum of the measures
of the exterior angles of any n-gon is
Use this information
________.
to complete the final
360
column of your polygon
sum chart!
measure
of one
Corollary: The
exterior angle of any regular n-gon is
360
____________.
n
Mrs. McConaughy
Geometry
8
Solving Statement Problems Using
Polygon Exterior Angle Sum Theorem
Algebraic Expressions Algebraic Equations
(Chart)
“How many sides…?”
Sum of
exterior
angles
360
Measure of
each angle
if regular
360
n
How many sides does a
regular polygon have if
each exterior angle
measures _____?
360 =
n
Geometry
KEY: Translate Words
 Symbols
Mrs. McConaughy
9
Sample Problems
 a. What is the sum of the measures of the
exterior angles of a decagon?
 b. What is the measure of each exterior
angle of a regular decagon?
 c. (How many sides) does a regular polygon
have if the measure of one exterior angle is
36?
Mrs. McConaughy
Geometry
10
Assume that all polygons are regular to
complete the chart below:
NUMBER OF SIDES
6
SUM OF INTERIOR
ANGLES
MEASURE OF EACH
EXTERIOR ANGLE
156
90
MEASURE OF EACH
INTERIOR ANGLE
Mrs. McConaughy
Geometry
R
E
A
D
135
11
Special Case: Exterior
Angle in a Triangle
Remote interior
angles
Aa
Exterior angle
m
b
B
c
x=m
x
C
a+m
D
b
EXTERIOR ANGLE CONJECTURE: The measure of an
exterior angle of a triangle equals the sum of the two
Mrs. McConaughy
Geometry
12
remote interior
angles.
Final Check: Now, try these
problems which follow without
any help!
Mrs. McConaughy
Geometry
13
Find the measure of ONE exterior angle of
a regular 20-gon.
sum of the exterior angles

number of sides
360

20
18°
Mrs. McConaughy
Geometry
14
The sum of the measures of five interior
angles of a hexagon is 625. What is the
measure of the sixth angle?
95°
Mrs. McConaughy
Geometry
15
Homework Assignment
Polygon Exterior Angle Supplemental
WS, plus textbook: _____________
Mrs. McConaughy
Geometry
16