Objectives(2):
Students will be able to find the sum of
measures of the interior angles of a polygon.
Students will be able to find the sum of the
measures of the exterior angles of a polygon.
Essential Questions:
Explain the formula (n-2)180.
Why is the sum of the exterior angles of any
polygon always 360 degrees?
Polygons
Polygons
Triangle – 3 sides
Quadrilateral – 4 sides
Pentagon – 5 sides
Hexagon – 6 sides (think hex-six)
Heptagon – 7 sides
Octagon – 8 sides
Nonagon – 9 sides (think non-nine)
Decagon – 10 sides (think decimal-ten)
Dodecagon – 12 sides
Interior Angles
An interior angle is an angle inside the
polygon.
Exterior Angles
An exterior angle is the angle between
any side of a shape and a line extended
from the next side
Polygon Angle-Sum Theorem
The sum of the measures of the interior
angles of an n-gon is (n-2)180.
Example 1
Example 1
Example 2
The sum of the angle measures of a polygon with n
sides is 1080. Find n.
(n-2)180 = 1080 divide by 180
n-2 = 6 add 2
n=8
To find the measure of each interior
angle of a regular polygon, divide the
total by the number of angles/sides.
Example 3
What is the measure of each angle of a hexagon?
Polygon Exterior Angle-Sum Theorem
The sum of the exterior angles of any polygon,
regardless of the number of sides is always 360
degrees.
Every circle has a measure of 360
degrees. Since a regular polygon can
be circumscribed by a circle, the
measure of the exterior angles is
360 degrees
Finding a missing angle of a polygon.
Example 4
To find the measure of one exterior
angle of a regular polygon, divide 360 by
the number of angles/sides.
Example 5
What is the m∠1 in the regular octagon
below?
360/8 = 45