Transcript 3.4 Polygon Angle Sum Theorems

10/28 with practice on 10/29
I
can name and classify a
polygon given the number of
sides and vertices.
 I can find the interior angles of a
polygon using the Polygon Angle
Sum Theorem
 I can find the exterior angle of a
polygon using the Polygon
Exterior Angle Sum Theorem
 Polygon
: a polygon is a closed
plane figure with at least three
sides that are segments. The
sides intersect only at their
endpoints.
 To
name a polygon, you
must name the vertices
consecutively
 EX:
 Convex
polygon: Has no
diagonals with points outside
the polygon.
 Concave polygon: Has at least
one diagonal with points
outside the polygon.
 EX

Part a is Convex
part b is Concave
Polygon Classification
3
sides 4 sides 5 sides 6 sides-
Polygon Classification(cont’d)
7
sides  8 sides  9 sides  10 sides  12 sides  N sides -
 Polygon
Angle Sum Theorem:
The sum of the measures of
the interior angles of any
polygon is (n – 2)180, where n
is the number of sides.
Ex.
What is the sum of the measures of angles of a
Decagon?
Pentagon?

 Find
the sum of the
measures of angles of an
octagon

Find x
 The
sum of the measures of
the interior angles is 720.
How many sides does it
have?
 Hint:
Work backwards
 Polygon
Exterior Angle Sum
Theorem: The sum of the
exterior angles of a polygon
is 360 degrees. ALWAYS!


An Equilateral polygon has all sides
congruent.
An Equiangular polygon has all angles
congruent.
The following is SUPER
IMPORTANT!!!
 A regular polygon has all
equal angles and equal sides.
 What
is the measure of an
exterior angle of a regular
hexagon?
 What
is the measure of an
interior angle of a regular
dodecagon?

The following is a regular polygon, find the
missing measures
In a regular polygon, the
sum of an interior angle
and exterior angle is 180°


Homework
In packet 3-4
 Warmup
– Grab your book
 For a regular nonagon
◦ What is the measure of an interior
angle?
◦ What is the measure on an exterior
angle?

Go over 3-4 Packet.
 P.147
#16-21
 3-4
worksheet practice