Name
Date
Angles and Polygons
Period
13.3
What is a polygon?
Make triangles out of the regular polygons!
Type of
polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Picture of
regular
polygon
# of
Sum of
angles/sides interior
angles
Measure of Measure
1 interior
of 1
angle
exterior
angle**
**How to find the exterior angle of a regular polygon:
First way is to find the measure of 1 interior angle and
subtract it from
.
Second way is to remember that the sum of the exterior
angles always adds up to
. Thus
.
Sum of the measure of the interior angles of a n-gon:
(n - 2) ∙ 180
n = # of sides or angles
To find the measure of an interior angle of a regular n-gon:
(𝒏−𝟐)𝟏𝟖𝟎
𝒏
n = # of sides or angles
This is simply the sum of the interior angles divided by the number of angles.
Practice:
1.
a. Find the sum of interior angles of the following regular polygon.
b. Can you find the measure of one interior angle? Why or why not?
c. If you said yes to b, then what is the measure of one interior angle?
2.
a. Find the sum of interior angles of the following polygon.
b. Can you find the measure of one interior angle? Why or why not?
c. If you said yes to b, then what is the measure of one interior angle?
13.
14.
Find the sum of the interior angles of the polygon.
15.
Find the measure of x.
a.
16.
a.
b.
Find the missing values.
b.
c.
17. The stained glass window is made with polygons. Each shaded figure is a
regular polygon. Find the values of x and y.