Name _ ______________________
Regular Polygon
Shape
Name of
Polygon triangle
Number of
Sides
3
Number of triangles
1
Sum of Interior
Angles
180
Measure of one angle
60 square 4 2 360 90 pentagon 5 hexagon 6 heptagon octagon nonagon
7
8
9 decagon 10
3
4
540 108
720 120
5 900 128.6
6 1080 135
7 1260 140
8 1440 144

What is the rule or formula for finding the sum of the measures of the interior angles of a polygon?
Rule: (n -2)180
What is the rule or formula for finding the measure of an interior angle of a regular polygon?
Rule:
(𝑛−2)180 𝑛
There are two types of problems that arise when using this formula:
1. Questions that ask you to find the number of degrees in the sum of the interior angles of a polygon.
2. Questions that ask you to find the number of sides of a polygon.
Hint: When working with the angle formulas for polygons, be sure to read each question carefully for clues as to which formula you will need to use to solve the problem. Look for the words that describe each kind of formula, such as the words sum, interior, each, exterior and degrees.
Example 1: Find the number of degrees in the sum of the interior angles of an octagon.
An octagon has 8 sides. So n = 8. Using the formula from above, 180(n - 2) = 180(8
- 2) = 180(6) = 1080 degrees.
Example 2: How many sides does a polygon have if the sum of its interior angles is 720°?
720 = (n – 2) 180
Divide both sides by 180
720
180
=
(𝑛−2)180
180
4 = n – 2
Add 2 to both sides n = 6