Download Math Content – Sum of Interior Angles

The Interior Angles of Polygons
Jessica King-Instructional Presentation
Objective
 To model the interior angles of polygons
 To apply the formula of the sum of interior angles
accurately
What Is A Polygon?
 A polygon is a two-dimensional shape made of straight line
segments, and the shape is closed.
 A closed shape means that all sides are connected
Interior Angles of Polygons
 Definition: An interior angle is an angle inside the
shape
Sum of A Triangle’s Interior
Angles
The Interior Angles of a Triangle add up to 180°
Sum of A Quadrilateral’s
Interior Angles
A quadrilateral
can be drawn as
two triangles…
So the Sum of the
Interior Angles of
a Square is
180+180 = 360°
Sum of the Interior Angles of
a Polygon with n number of
sides
We can draw line segments from one
angle to another to create multiple
triangles out of each polygon…
Activity: Constructing Triangles in a
Polygon
The Sum of Interior Angles
Formula
The sum of interior angles
=180°(n-2)
Where n is the number of
sides of the polygon
Example
 What is the Sum of the Interior Angles of an Octagon?
An octagon has 8 sides
8=n
Sum of Interior Angles
= 180(n-2)
=180(8-2)
=180(6)
=1080°
The Sum of the Interior Angles of an Octagon is 1080°