+

Polygon Angle Sum Theorem (3.4)Objective:To classify polygons, and to find the sums of interior and exterior angles of polygons

+Polygon

Closed plane figure

At least 3 sides that are segments

Sides intersect only at endpoints

Adjacent sides are NOT collinear

POLYGONS NOT POLYGONS

+To Name a Polygon…

1. Start at any vertex

2. List vertices consecutively

Example: Name the polygon. Name the sides and angles.

Name ____________________________

Sides _____________________________

Angles ____________________________

+Common Polygons

SIDES NAME

3 Triangle

4 Quadrilateral

5 Pentagon

6 Hexagon

8 Octagon

9 Nonagon

10 Decagon

12 Dodecagon

n n-gon

+Concave vs. Convex

CONCAVE Polygon CONVEX Polygon

• At least one diagonal outside polygon

• Has an indent in at least one edge (“caves in”)

• No diagonal with points outside polygon

• Has no indents in any edges

+Polygon-Angle Sum Theorem

The sum of the measures of angles in an n-gon:

Example: Find the sum of the measures of a 15-gon.

+Finding missing angle measures

1. Figure out what the sum of the interior angles should be

2. Add up expressions and set them equal to the sum from part one.

Example #1:

+Examples

#2. The sum of the measures of a given polygon is 720. How many sides are in the polygon?

#3 Pentagon ABCDE has 5 congruent angles. Find the measure of each angle.

+Polygon-Exterior Angle Sum Theorem

The sum of the measures of exterior angles of a polygon is ALWAYS

YouTube Video

Example #4:

What is the sum of the exterior angles for a 500-gon?

+ EQUILATERAL POLYGON: All sides congruent

EQUIANGULAR POLYGON: All angles congruent

REGULAR POLYGON: Equilateral AND Equiangular

ONE Interior Measure ONE Exterior Measure

+More Examples…

#5. The sum of the measures of angles of a polygon with n sides is 1980. Find n, the number of sides.

#6. Find the measures of one interior angle and one exterior angle of a REGULAR hexagon.

+Last One!

#7. The measure of an exterior angle of a regular polygon is 30. What is the measure of an interior angle? How many sides are there?