Download Section 3-5 Angles of Polygons

Section 3-5 Angles of Polygons
Objective:
•Recognize and name the convex
polygons and regular polygons.
•Find the measures of the interior
angles and exterior angles of convex
polygons.
Standard 2.9 Concepts in Geometry
The left five figures are polygons. The
right figures are not. Using this
knowledge, write the definitions or
qualities a polygon can/cannot have.
Polygons
 Made up of segments (thus no curves)
 Must have three or more sides
 Can be non-convex but we focus on
convex.
– Ex. Non-Convex
where there is at
least one line
that is interior
Convex vs. Non-Convex
Naming Polygons
 Number of Sides
 Name
3
4
5
6
8
10
n
Triangle
Quadrilateral
Pentagon
Hexagon
Octagon
Decagon
n-gon
How many different triangles can be
forms by drawing diagonals through the
following polygons
Definition of diagonal: interior segment
from one vertex to another.
6 sides & 4
triangles
8 sides & 6
triangles
4 sides &
2 triangles
3 sides &
1 triangles
Investigation-Fill in the chart and
make a conjecture:
#of sides
3
4
5
6
7
8
9
10
15
20
n
#of
angle sum
Theorem 3-13
The sum of the measures of the
angles of a convex polygon with n
sides is (n-2) 180
Interior Angle Thm
Theorem 3-14
The sum of the measures of the
exterior angles of any convex
polygon, one angle at each, is 360
Exterior Angle Sum Theorem
Ex. If a polygon has 22 sides. Find
the interior and exterior angle sum.
 Interior sum
(n-2) 180
(22-2) 180
(20) 180
3600
 Exterior sum
360
Regular Polygons
 Regular polygons are equiangular and
equilateral.
 Thus all their interior angles are ______
and all their sides are _______.
Example 1
All regular 7 sided figures
have interior angle
measures of ____ and
exterior angle measures of
_____.
Answers: int = 128.5 ext = 51.5
Example 2
 All regular 6 sided figures
have interior angle
measures of ____ and
exterior angle measures of
_____.
 Answers: int = 120° and ext = 60°.
 Group Work
CE p. 103 #1-6 and 9
 HW
WE p.104 #1-23 all