6.1 - Polygon Angle Sum Theorems

6.1 - Polygon Angle Sum Theorems

By Steve Dull

Objective

• To find the sum of the measures of the interior angles of a polygon

• To find the sum of the measures of the exterior angles of a polygon​

Vocabulary

• A polygon is a closed two-dimensional figure formed by three or more straight segments called sides.

• The points where two sides meet are called vertices.​

• An n-gon is a polygon with n sides​

​Complete the table and look for a pattern to find the sum of the degrees in any polygon.

​

Let's practice:

Find the sum of the interior angles of a 15-gon:

S = (n-2)*180

​

Let's practice:

Find the sum of the interior angles of a 15-gon:

S = (n-2)*180

=​ (15-2)*180

​

Let's practice:

Find the sum of the interior angles of a 15-gon:

S = (n-2)*180

=​ (15-2)*180

​ = (13)*180

= ​2340 degrees

​

Multiple Choice

What is the sum of the interior angles of a 21-gon?

• $$360\degree$$  

• $$3420\degree$$  

• $$3780\degree$$  

• $$21\degree$$  

Open Ended

Explain how to find the sum of the interior angles of a 36-gon:

Open Ended

What is the sum of the interior angles of a 48-gon?

Vocabulary

​Regular polygon

A polygon having equal sides and equal angles is a regular polygon.

​

(Example: a square is a regular quadrilateral).​

So to determine the measure of an interior angle of a regular pentagon, first determine the sum of the angles:

(5-2)*180 = 3* 180 = 540 degrees;

​

​Then divide the sum by the number of sides:

​540/5 = 108 degrees.

Open Ended

What is the measure of an interior angle of a regular 18-gon?

Open Ended

What can you conclude about the sum of the exterior angles of a polygon?

Find a friend and let's practice