What is a Polygon?• A polygon is a closed figure that is the

union of line segments in a plane. 

• A polygon has three or more sides.

• A polygon has the same number of angles as sides.

Concave or Convex  * In a convex polygon, each interior angle measures less

than 180 degrees. 

*Concave polygons "cave-in" to their interiors, creating at least one interior angle greater than 180 degrees.

Regular or not Regular

• A polygon is regular if all the sides and angles are equal in measure

Types of PolygonsPolygon Graphic Sides Angles Diagonals

(from one vertex)

Triangles Degrees

Polygon Graphic Sides Angles Diagonals Triangles Degrees

Polygon Graphic Sides Angles Diagonals Triangles Degrees

Interior Angles• Sum of Interior Angles of a Polygon= 180(n - 2)

(where n = number of sides)

Example 1:  Find the number of degrees in the sum of the interior angles of an 14 – sided polygon.

Example 2: Find the number of degrees in the sum of the interior angles of an 20 – sided polygon,

Interior Angles• To find missing angles in a polygon

– 1. Find the total number of degrees in polygon.

– 2. Set up an equation equal to the number of degrees.

– 3. Solve equation.

Example

87°

x°

99° 99°

105°

Interior Angles• Each interior angle of a regular polygon = 

where n = the number of sides in the polygon

Example 1: Find the number of degrees in each interior angle of a regular dodecagon.

Example 2: Each interior angle of a regular polygon measures 135°.  How many sides does the polygon have?

• Find the value of x.

9x 9x

9x 9x

12x 12x

Exterior Angles• An exterior angle of a polygon is an angle that forms a

linear pair with one of the angles of the polygon. For the hexagon shown at the left, <1

and <2 are exterior angles for that vertex. 

Formula:Sum exterior angles of any polygon = 360°(using one exterior angle at a vertex)

Formula:  Each exterior angle (regular polygon) =

1

2

Exterior Angles• Example 1: Find the sum of the exterior angles of:

1. pentagon

2. decagon

3. a 15 sided polygon

4. a 7 sided polygon

* Example 2: Find the measure of each exterior angle of a regular hexagon.

http://www.regentsprep.org/Regents/math/geometry/GG3/PPoly1.htm

http://www.regentsprep.org/Regents/math/geometry/GG3/PPoly2.htm

http://www.regentsprep.org/Regents/math/geometry/GG3/PPoly3.htm