C40 Exterior Angle Sum Conjecture:

1
C-40 (Exterior Angle Sum Conjecture)

• The sum of the measures of one set of exterior
  angles is

360
2
What is the expression used to find the sum of
the interior angles of any n-gon?
180(n-2)
3
You know how to find the sum of the interior
angles of any polygon 180(n-2). Think about
an expression to find the measure of each
angle in an equiangular polygon.
4
180(n-2)
This tells you the sum..
Divide the sum by the number of angles and you
have the measure of each angle.
5
This also works
6
C-41 (Equiangular Polygon Conjecture)

• The measure of each angle of an equiangular n-gon
  can be found using

7
What is the measure of each interior angle of a
regular triangle?
n3
8
Each interior angle of a regular triangle is 60.
9
What is the measure of each interior angle of a
regular pentagon?
n5
10
What is the measure of each interior angle of a
regular hexagon?
120
11
What is the measure of each interior angle of a
regular octagon?
135
12
A regular n-gon has interior angle measures of
160. The n-gon has how many sides?

• .solve for n

13
(No Transcript)
14
A regular polygon with interior angle measures of
160 has 18 sides.
15
A regular n-gon has interior angle measures of
165.6. This n-gon has how many sides?

• .solve for n

16
(No Transcript)
17
A regular polygon with interior angle measures of
165.6 has 25 sides.
18
A regular n-gon has interior angle measures of
172.8. The n-gon has how many sides?

• 50 sides