7.1A: Polygon Angle Theorems

Geometry
4/4/2024

Target 7.1A: Polygon Angle Theorems

Classwork for Today

1) You need to get out your notes from yesterday. If you were gone yesterday or have lost your notes, they are available in the back of the room where you normally pick up the day's notes.
2) Today's lesson will go through:
Finishing yesterday's notes, Setting you up for success on the homework, and go through problems that are on the Practice Test that you will not get.
3) You are expected to write notes down on your notes sheet and complete the homework problems.
4) You will need a calculator. Because several of mine are missing, remember you can ask to borrow a calculator from another teacher or for today you may use your Chromebook for a calculator. You may NOT use your phone!
5) Lastly, remember the Quiz is tomorrow. You will need to actively engage in the lesson to be successful.
6) If you do not finish this during class, you need to finish it before class on Friday.

GOOD LUCK! Hope you enjoy!

Multiple Select

Let's start with a review question: Which of the following are polygons?

Choose all that apply.

(Recall that polygons are closed 2-dimensional shapes that are made of three or more straight segments that only intersect exactly two other segments)

Multiple Choice

More Review:

How many sides does a pentagon have?

• 3

• 4

• 5

• 6

Multiple Choice

Even More Review:

How many sides does an octagon have?

• 8

• 9

• 10

• 11

Multiple Choice

I'm a math teacher... Of course I'm going to give you more review!

How many sides does a decagon have?

• 9

• 10

• 11

• 12

Equilateral- Any Polygon whose sides are all congruent

Equiangular- Any polygon whose angles are all congruent

Regular- Any polygon that is both equilateral AND equiangular

​

Regular Polygons

Polygon Interior Angles Theorem:
This is the formula you use when you want to find the sum of the interior angles of any polygon.

Think back to yesterday when we found the number of triangles in a polygon and multiplied that by 180 degrees (since each triangle has 180 degrees).

What We Learned Yesterday

Look at how they do this problem. The next one will be on your own!

Textbook Example

Fill in the Blanks

Practice Test Question:

Hint (write this down on a scrap piece of paper)

Classify the polygon shown by its number of sides.

Math Response

Practice Test Question

Again, I'd write this down!

Find the sum of the interior angle measures of the polygon shown below.

Type answer here

Correct Answer: 1620

Deg^°

Rad

Mr. Schenewerk

Now... go ask your sub for today's homework.
You will only get today's homework if you ask for it!

Math Response

On your 7.1 Homework, let's look at #2A.

Find the measure of each of the following for a regular convex nonagon.

A) Sum of the interior angles.

Type answer here

Correct Answer: 1260

Deg^°

Rad

Geometry 7.1 Practice Quiz #3 question | Loom

You can open this webpage in a new tab.

Copy link

Open in new tab

Math Response

Now, let's go back to your homework assignment.

Let's look at #4.

Your answer will have a decimal point. Don't round.

Type answer here

Correct Answer: 100.5

Deg^°

Rad

7.1A: One Internal Angle | Loom

You can open this webpage in a new tab.

Copy link

Open in new tab

Math Response

Notes: Middle Example

Write this down in your notes!

Find the measure of one interior angle of the regular polygon shown.

Type answer here

Correct Answer: 108

Deg^°

Rad

Math Response

Back to the Practice Test:

Find the measure of one interior angle of the polygon shown.

Your answer will be a decimal.

Round to 2 decimal points.

Type answer here

Correct Answer: 147.27

Deg^°

Rad

Loom Message - 3 April 2024 | Loom

You can open this webpage in a new tab.

Copy link

Open in new tab

Math Response

Now try #3 B in your homework:

Find the measure of one interior angle.

Type answer here

Correct Answer: 135

Deg^°

Rad

Notice that the exterior angles of any polygon adds up to 360 degrees.

This is why as we increase the number of sides of a regular polygon it increasingly looks like a circle.

7.1 Practice Quiz #1D | Loom

You can open this webpage in a new tab.

Copy link

Open in new tab

Math Response

Now try #2C on your homework.

Find the measure of one exterior angle of a regular convex nonagon.

Type answer here

Correct Answer: 40

Deg^°

Rad

Math Response

Now try #3C on the homework.

Find the measure of one exterior angle of the regular polygon shown.

Type answer here

Correct Answer: 45

Deg^°

Rad

The next slide is the next to last example in the notes.

Final Example of 7.1A Notes | Loom

You can open this webpage in a new tab.

Copy link

Open in new tab

Math Response

Finally, look at #5 on your Homework.

Find the value of x.

Type answer here

Correct Answer: 11

Deg^°

Rad

Math Response

Now let's look at a Practice Test Question.

Find the value of x.

Type answer here

Correct Answer: 32

Deg^°

Rad