Polygons
Notes Page
A polygon is a closed figure that has three or more sides.
A regular polygon is a polygon that is both equilateral and equiangular.
Sum of the Interior Angles of a Polygon:
The formula for the sum of the interior angles of a polygon is:
180(n-2), where n represents the number of sides in the polygon.
If the problem asks you to find the measure of one angle of a regular polygon, use the formula above and divide by the number of sides in the polygon. *Remember* -
This formula can only be used for regular polygons.
Formula: 180(n-2)/n
Examples:
1.
Find the number of degrees in the sum of the interior angles of an octagon.
2.
How many sides does a polygon have if the sum of the interior angles is
720˚?
3.
How many degrees are there in the sum of the interior angles of a nine sided polygon?
4.
If the sum of the interior angles of a polygon equals 900˚, how many sides does the polygon have?
5.
What is the measure of the interior angle of a regular decagon?
6.
What is the measure of the interior angle of a regular pentagon?
Exterior Angles of Polygons:
An exterior angle of a polygon is an angle that forms a linear pair with one of the angles of the polygon.

The sum of exterior angles of a polygon = 360˚. Therefore, to find the measure of one exterior angle of a regular polygon is: 360/n.
Examples:
1.
Find the measure of each exterior angle of a hexagon.
2.
The measure of each exterior angle of a regular polygon is 45˚. How many sides does the polygon have?
3.
How many degrees are there in the sum of the exterior angles of a dodecagon?
4.
What is the measure of one exterior angle of a decagon?
5.
What is the measure of one exterior angle on a stop sign?