section 3-5 angles of a polygon. polygon means: “many-angled” a polygon is a closed figure...

Section 3-5Angles of a

Polygon

Polygon

• Means: “many-angled”

• A polygon is a closed figure formed by a finite number of coplanar segments

a. Each side intersects exactly two other sides, one at each endpoint.

b. No two segments with a common endpoint are collinear

Ex #1

Examples of polygons:

Ex#2

Two Types of Polygons:

1. Convex: If a line was extended from the sides of a polygon, it will NOT go through the interior of the polygon.

Ex #1

2. Nonconvex: If a line was extended from the sides of a polygon, it WILL go through the interior of the polygon.

Ex#2

Polygons are classified according to the number of sides they have.

*Must have at least 3 sides to form a polygon.

Special names

for Polygons

Number of Sides

Name

3 Triangle

4 Quadrilateral

5 Pentagon

6 Hexagon

7 Heptagon

8 Octagon

9 Nonagon

10 Decagon

n n-gon*n stands for number of sides.

Diagonal

• A segment joining two nonconsecutive vertices

*The diagonals are indicated with dashed lines.

Definition of Regular Polygon:

• a convex polygon with all sides congruent and all angles congruent.

Interior Angle Sum Theorem

• The sum of the measures of the interior angles of a convex polygon with n sides is

S = 180 (n - 2)

One can find the measure of each interior angle of a regular polygon:

1. Find the Sum of the interior angles

2.Divide the sum by the number of sides the regular polygon has.

S = 180 (n - 2)

n

S

One can find the number of sides a polygon has if given the measure of an interior angle

n

n 2180

Exterior Angle Sum Theorem

• The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360.

One can find the measure of each exterior angle of a regular polygon:

360

n = exterior angle

or

360

exterior angle = n

One can find the number of sides a polygon has if given the measure of an exterior angle