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Determining the Sum of the Angles in a Polygon

The Trigs

This song is available on Triangle Head by The Trigs.

This song explores the formula for finding the sum of the interior angles in a polygon. First it talks about what the formula is and then delves into why.

How do I find the summation
of all the angles inside of
The polygon that I am looking at?

Well, that's easy and here is why:
It's a pattern that's easy to apply
There's just three steps and here they are:

Step 1: Count up all the sides
Step 2: Subtract the number 2
Step 3: Multiply by 180
And then you're done

Let's talk about polygons
Let's talk about names and sides
Let's talk about how to find the angles and their measurements inside
Let's talk about triangles
Let's talk about vertices
Let's talk about how to find them all so we can solve them all with ease

So now we need to find out why
This pattern works all of the time
It's got something to do with triangles

Ask yourself how many times
Can I draw non-intersecting lines
On the inside of my polygon?

You need to pick just one vertex
And draw all of the lines you can
Make sure they don't intersect
And then you're done

Now that you've drawn all your lines
Count the triangles inside
You'll find that you've always got two less than there are sides
And how many degrees are there in a triangle?
That's why you multiply by 180

See more of our Songs that Teach about Advanced Math

Many thanks to The Trigs for permission to display these lyric excerpts.
© The Trigs. All rights reserved. Used with permission.

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