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### Section 3.5 – P lyg nAngle-Sum Theorems

Created by Leon Tyler Funchess

The Introduction

Okay, so I had an introduction on the wikipage. But now this is the real deal.

Hello, how are you? I see you’ve come to my page to visit the magical wonders of polygon angle-sums. They may seem intimidating at first, but I’m here to blast that intimidation out of the way. Welp, here we go!!!!!

For readers, press the next arrow button four times before reading for maximum effectiveness. Baby steps… let’s start off with some basic skills you’ll need.

- Okay, so the first thing you’ll need to know is how to add. I sure hope you can do that.
- Next you’ll need to know what a polygon is!
- A polygon is a figure that has more than 3 sides, where all of these sides are segments which in turn close the figure; the shape has no openings nor do any of the sides cross/intersect.
- The final basic skill you’ll need to properly do anything in this section is to be able to name polygons.
- You’ll need to be able to name it by the letters around it. The polygon up here would be considered polygon ABCDE (or EDCBA if you’re a hipster). You also need to be able to name its sides, (sides AB, BC, CD, DE, EF and FA) and its vertices/angles (they’re the same thing in this situation) [Angles A, B, C, D, E, and F]

A

B

This sir, is a polygon. Six sides, no openings or closings. Perfecto.

C

F

D

E

For readers: press the next arrow button three times before you read for maximum effectiveness.Next: Classifying Polygons

- I seem to have recovered a chart showing the

name of polygon, named by the number of the sides.

(I have no idear where I found this! ;D)

- [This is one way how you can classify polygons, btw]
- Another way to classify polygons is by calling them

either convex or concave.

concave

THEY’RE BOTH POLYGONS THOUGH, SO DON’T WORRY

Convex

Some diagonals of the polygon have points on the outside, that’s not okay!

All diagonals of the polygon have points on the inside of the polygon.

Okay enough with that introductory stuff, let’s get to the meat of this lesson.

I know you’re probably saying, “ugh, ANOTHER THEOREM?!” but don’t be afraid, this is one of the few that has actual MATH incorporated into it. But he is the mighty polygon angle-sum theorem. I’ll explain it in detail.

------ » Okay, so the first 12 words of this theorem is basically self-explanatory, if that’s the word.. But the last part might confuse you. (n-2)180 is actually saying the quantity of the number of sides minus two times 180°. So for example, lets say you want to find out the angle sum of a pentagon. By referring to the chart on slide 4, you will find out that a pentagon has 5 sides. So the substitute for n in the equation is 5, and all you do from there is plug + chug!!! (5-2)180 = 3(180) = 540°. Boomshakalaka. You have the angle sum of a pentagon, easy as Parcheesi.

Wait guys, there’s one thing left I have to show you!

- Sorry it’s another theorem, but it is important. It says that no matter what polygon is, the measure of its exterior angles will always be 360°.
- The exterior angle is achieved by extending a vertex a little outwards, and the measure of the new angle that is formed is one of the exterior angles. A polygon has the same number of exterior angles as it has regular angles and sides.

Readers, press the next arrow button two times before reading for maximum effectiveness. Now here comes the fun part, the part where I evaluate you!!!

Evaluation for adding.

- 2+2=?
- 3+190234=?
- 4²+2²+œ=?

Evaluation for knowing what a polygon is.

- Is this a polygon?
- What about this?
- This?
- You wont

get this

one.

Evaluation for naming a polygon.

I think you guys are capable enough to be able to do this w/o any evaluation…

Readers, press the next arrow button two times before reading for maximum effectiveness. Haha, that last slide was just a little joke. Back to seriousness.

Evaluation on theorem 3-14

- What is the angle sum for this polygon?
- This one?

Evaluation on theorem 3-15

What is the exterior angle sum for all these polygons?

2a

2c

heptagon

2b

Readers, press the next arrow button three times before reading for maximum effectiveness. Are you ready for this?I’m going to show you the answers.

Okay, here’s the first part….

4

No. it crosses.

190237

Lol you can’t add letters and numbers together!!

yes

yes

Heart: no

Arrow behind heart: yes

Readers, press the next arrow button three times before reading for maximum effectiveness. Next set of answers!!

Here goes!

(4-2)180=360°

(4-2)180=360°

(10-2)180=1440°

360° for all of ‘em.

(7-2)180=900°

Readers, press the next arrow button two times AFTER reading for maximum effectiveness. Phew! Are you glad this is over? Me and you both!

We learned a lot today. Two theorems. How to classify a polygon. How to name a polygon.

Hopefully my unique teaching style will help this stick to your mind? (between me and you, It won’t stick in mines! Lol) And hopefully this study guide will help your preparations for the midterms!!!!!!

GOOD LUCK EVERYONE!!!!!!!!!!

And thank you to everyone who read my study guide, it helps me stay up for business! :P and if I happened to forget something you felt was important in this section, please comment! Suggestions and all that other good stuff is also good too. Thanks again!

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