Section 2.5

Polygons

Polygon	Number of sides
Triangle	3
Quadrilateral	4
Pentagon	5
Hexagon	6
Heptagon	7
Octagon	8
Nonagon	9
Decagon	10

Number of Diagonals

Triangle

0 Diagonals

Quadrilateral

2 Diagonals

Pentagon

5 diagonals

Hexagon

9 Diagonals

Polygon	Diagonals
Triangle	0
Quadrilateral	2
Pentagon	5
Hexagon	9

Formula for finding the number of diagonals of a polygon

Example 1

Find the number of diagonals of a polygon with 20 sides

Finding the sum of the interior angles of a polygon

Number of sides of the polygon	Sum of the interior angles
3	180º
4	360º
5	540º
4	720º

Formula for finding the sum of the interior angles

Examples

1) Find the sum of the interior angles of a decagon

2) Find the sum of the interior angles of an octagon

A regular polygon is a polygon with all sides and all angles that are congruent.

Finding the measure of the interior angle of a regular polygon

Examples

1) Find the measure of the interior angle of a regular octagon

2) Find the measure of the interior angle of a regular decagon

Finding the measure of the exterior angle of a regular polygon

3) Find the measure of the exterior angle of a regular decagon

Examples from page 102

14) Find the sides of a polygon has if the sum of the interior angle is:

a) 1980º

b) 2340º

16) Find the number of sides a regular polygon has if the measure of each interior angle is:

a) 150º

b) 168º

Polygon	Number of sides	Diagonals	Sum of the interior angles	Sum of the exterior angles	Measure of interior angle	Measure of exterior angle
Quadrilateral	4			360º	90º	90º
Pentagon	5	5	540	360	108	72
Hexagon	6	9	720	360	120	60