Date ______________________________
Notes: Interior and Exterior Angle Sum Theorems
Essential Question:
 What is the difference between “Regular” and “Irregular” Polygons?
Interior Angle
Sum Theorem
In convex polygons, the interior angle sum follows a pattern to which we can
create a formula to work for all polygons. Lets see if we can come up with this
formula together.
EXPLORE
In the figures below, draw in all of the diagonals from a single vertex.
a.
b.
c.
What is shape created when we draw in those diagonals inside the figure?
What do we know about that shape and its interior angles?
How can we use this information to create a formula that works for all polygons?
(HINT: Use the number of sides)
Test the Theory
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
N-gon
# of sides
FORMULA - _________________________
# of Triangles
Sum of Interior ’s
Using the Interior
Angle Sum
Theorem
Use the formula to answer the following questions.
1. What is the sum of the interior angles of a convex heptagon?
2. How many sides does a regular polygon have if the sum of the interior
angles is 2880 degrees.
3. What is the measure of one interior angle in a regular Dodecagon?
Exterior Angle
Theorem
The sum of the measures of the exterior angles of a convex polygon is
ALWAYS 360. ALWAYS!!!!!!
1. What is the sum of the exterior angles of a convex pentagon?
2. Find the measure of one exterior angle of a convex pentagon?
3. Use the exterior angle theorem to solve for y?
Summary: