By: Thomas SeleyBy: Thomas Seley

20052005©©

Obtuse Obtuse AnglesAngles

The Basics of Angles

Reflex Angles

Acute Angles

Right Angles

2.2.

1.1.

5.5.

4.4.

3.3.

6.6.

Move Move through the through the

topics at your topics at your own paceown pace

The The numbers are numbers are

just just suggestions.suggestions.The ProjectThe Project

Right AnglesRight Angles

• A right angle is a “square corner”.

• A right angle is 90°.

• A right angle looks like this:

More About Right Angles!More About Right Angles!

• Only right angles have a square at the vertex.

• Right angles can be rotated many ways.

• But as long as there is a square corner, the angle is a right angle.

Let’s Take a Quiz!Let’s Take a Quiz!

Is this a right angle?

Yes No

Awesome!!!

Let’s see how you do on the next question.

Sorry…Sorry…

Remember that right angles often have a square at the vertex.

Let’s try again.

How about this angle? Is it a right angle?

Yes No

Great!!!Great!!!

You really know your right angles!

Sorry…Sorry…

Remember:

If an angle is not a “square corner”, it is not a right angle.

Let’s try again.

Let’s try one more question…Let’s try one more question…

Fill in the blank: A right angle is _____ degrees.

A. 90°

B. 30°

C. 120°

B. 30°

C. 120°

B. 30°

C. 120°

Fantastic!!!Fantastic!!!

A right angle is always 90°.

Click here and choose a new area of angles to explore.

That’s too badThat’s too bad

A right angle is always 90°.

Let’s try again.

The Basics of AnglesThe Basics of Angles

• An angle is formed when two lines or two line segments meet at a point.

• Here’s an angle formed by 2 rays:

• Here’s an angle formed by 2 line segments:

More Basics of Angles…More Basics of Angles…

• This is the symbol for an angle:

• Angles are measured in degrees.

• For example, if an angle is 35 degrees, we write it like this:

35°Notice the symbol for degrees.

And More Basics of AnglesAnd More Basics of Angles

• All angles have a vertex.

• The vertex is like the “elbow” of the angle.

I’m a vertex.

How We Mark an Angle…How We Mark an Angle…

• Sometimes we make a curve at the vertex to show measurement.

• When the angle is a right angle, we often draw a square at the vertex.

45°

90°

Very Important Info!!!Very Important Info!!!

Even though we Even though we share the same share the same

vertex, I measure vertex, I measure a different angle a different angle than that than that green arc over there. arc over there.

I measure I measure a different a different angle than angle than

that that redred arc over arc over there. there.

Angles Are All Around UsAngles Are All Around Us

Click here to learn about the types of angles.

Acute AnglesAcute Angles

• An acute angle is greater than 0° and less than 90°.

• An acute angle is “more closed” than a right angle.

Right AngleRight Angle

““Square Corner”Square Corner”

Acute AngleAcute Angle

Acute AngleAcute Angle

Acute AngleAcute AngleAcute AngleAcute Angle

PacMan and the Acute AnglePacMan and the Acute Angle

• This is Pac-Man.

• Pac-Man’s mouth is an acute angle.

• Acute angle

• Isn’t Pac-Man cute?

• Acute

Let’s Take a Quiz!Let’s Take a Quiz!

Can you pick the acute angle?

A.

B.

C.

D.

Great!Great!

You really know your acute angles!

Sorry…Sorry…

• An acute angle is between 0° and 90°.

• An acute angle is “more closed” than a right angle.

Let’s Try Another QuestionLet’s Try Another Question

True or False: An acute angle is less than 90°.

True False

Sorry, Let’s Review Acute AnglesSorry, Let’s Review Acute Angles

• An acute angle is greater than 0° and less than 90°.

• An acute angle is “more closed” than a right angle.

Right AngleRight Angle

““Square Corner”Square Corner”

Acute AngleAcute Angle

Acute AngleAcute Angle

Acute AngleAcute AngleAcute AngleAcute Angle

Excellent!Excellent!

You’re You’re getting good getting good

at this!at this!

One More Question…One More Question…

Which one of these is an acute angle?

1.1.

2.2.

3.3.

4.4.

Great!Great!

You really know your acute angles!

Click here to Click here to check out other check out other types of angles.types of angles.

Sorry…Sorry…

• An acute angle is between 0° and 90°.

• An acute angle is “more closed” than a right angle.

Reflex AnglesReflex Angles

• Reflex angles are between 180° and 360°.

• A 180° angle is a straight line.

• A 360° angle is a completely closed angle.

• Reflex angles are in between.

180180°°

360360°°

Examples of Reflex AnglesExamples of Reflex Angles

270270°°

260260°°

240240°°

210210°°

335335°°

Let’s Check Your Reflexes!Let’s Check Your Reflexes!

Which one of these is an reflex angle?

1.1.

2.2.

3.3.

4.4.

4545°°

340340°°

9090°°

3030°°

Wow!!!Wow!!!

Great job! Now try one more.

Sorry, Let’s Review Reflex AnglesSorry, Let’s Review Reflex Angles

• Reflex angles are between 180° and 360°.

• A 180° angle is a straight line.

• A 360° angle is a completely closed angle.

• Reflex angles are in between.

180180°°

360360°°

Examples of Reflex AnglesExamples of Reflex Angles

270270°°

260260°°

240240°°

210210°°

335335°°

Let’s See If You Know This OneLet’s See If You Know This One

A reflex angle is…

A. Between 0A. Between 0°° and 90°. and 90°.

D. Between 90D. Between 90°° and 180°. and 180°.

B. Between 180B. Between 180°° and 360°. and 360°.

C. Between 90C. Between 90°° and 360°. and 360°.

Sorry, Let’s ReviewSorry, Let’s Review

• Reflex angles are between 180° and 360°.

• A 180° angle is a straight line.

• A 360° angle is a completely closed angle.

• Reflex angles are in between.

180180°°

360360°°

Examples of Reflex AnglesExamples of Reflex Angles

270270°°

260260°°

240240°°

210210°°

335335°°

Great Job! One More QuestionGreat Job! One More Question

The two lines below form two angles. Which The two lines below form two angles. Which angle is the reflex angle?angle is the reflex angle?

The Green One! The Orange One!

Sorry, Let’s ReviewSorry, Let’s Review

• Reflex angles are between 180° and 360°.

• A 180° angle is a straight line.

• A 360° angle is a completely closed angle.

• Reflex angles are in between.

180180°°

360360°°

Examples of Reflex AnglesExamples of Reflex Angles

270270°°

260260°°

240240°°

210210°°

335335°°

Stupendous!!!Stupendous!!!

You really know about reflex angles .

Click below to return to the main menu.

Obtuse AnglesObtuse Angles

• An obtuse angle is open more than a right angle.

• But an obtuse angle is more closed than a straight line.

• An obtuse angle is between 90° and 180°.

Angle DiagramAngle Diagram•This diagram This diagram shows the shows the different types of different types of angles from the angles from the starting point.starting point.

•Red shows acute Red shows acute angles.angles.

•Green shows Green shows obtuse angles.obtuse angles.

•Purple shows Purple shows reflex angles.reflex angles.

•Yellow shows a Yellow shows a right angle.right angle.

AcuteAcuteObtuseObtuse

ReflexReflex

I’m a right

angle.

Starting LineStarting Line

Note: An angle’s starting line is different every time. We judge the angle on how many degrees it opens up.

More About Obtuse AnglesMore About Obtuse Angles• Remember

this diagram?• The green The green

area shows area shows obtuse obtuse angles.angles. AcuteAcuteObtuseObtuse

ReflexReflex

I’m still a right angle

Starting LineStarting Line

Note: An angle’s starting line is different every time. We judge the angle on how many degrees it opens up.

Let’s Take a Quiz!Let’s Take a Quiz!

Can you pick the obtuse angle?

A.

B.

C.

D.

Sorry, Let’s Review Obtuse AnglesSorry, Let’s Review Obtuse Angles

• An obtuse angle is open more than a right angle.

• But an obtuse angle is more closed than a straight line.

• An obtuse angle is between 90° and 180°.

Sorry Sorry

• This one was tricky.

• We know the angle is not obtuse for 2 reasons.– The angle has a square at the vertex.– The angle is a “square corner”.

• Both of these facts make it a right angle.

Let’s try again.Let’s try again.

Great!Great!

Let’s try Let’s try another.another.

An Obtuse QuestionAn Obtuse Question

How many degrees are in a obtuse angle?

A. An obtuse angle is between 90 and 180 degrees.A. An obtuse angle is between 90 and 180 degrees.

B. An obtuse angle is between 0 and 90 degrees.B. An obtuse angle is between 0 and 90 degrees.

C. An obtuse angle is 90 degrees.C. An obtuse angle is 90 degrees.

D. An obtuse angle is between 180 and 360 degrees.D. An obtuse angle is between 180 and 360 degrees.

Sorry, Let’s Review Obtuse AnglesSorry, Let’s Review Obtuse Angles

• An obtuse angle is open more than a right angle.

• But an obtuse angle is more closed than a straight line.

• An obtuse angle is between 90° and 180°.

Way to Go!Way to Go!

Knowing how many degrees are in an obtuse angle is as important as knowing what it looks like.

A Truly Obtuse QuestionA Truly Obtuse Question

True or False: This angle is obtuse.

TrueTrue FalseFalse

• I have some good news and some bad news.• The Bad News: If you thought this was a reflex

angle, you were wrong.

• Pay attention to the measurement arc.

• The Good News: If the measurement arc was on the other part of the angle, it would be a reflex angle.

YES!YES!

You still knew it was an You still knew it was an obtuse angle even obtuse angle even

though it was rotated. though it was rotated. You are a clever kid!You are a clever kid!

The ProjectThe Project

• Your mission is to create a collage.

• You will use a large piece of paper.

• Divide the paper into 4 sections like this:

Right

Obtuse Reflex

Acute

•Label the four sections like this…

Making the Angles CollageMaking the Angles Collage

• Cut out pictures of the 4 types of angles.• Draw in the vertex, measurement arc, and lines

with a magic marker, crayon or paintbrush.• Make it beautiful.• We will post these in the hallway for the world to

see!

Click here for a small example.

Right

ReflexObtuse

Acute

Angle Collage CheckbricAngle Collage Checkbric

1. Did I write my name on the paper?2. Did I divide the paper into 4 sections?3. Did I label the sections: Right, Acute, Obtuse, and Reflex?4. Did I include at least 5 examples of each type of angle?5. Did I mark all lines or line segments? 6. Did I draw a dot for all the vertexes?7. Did I draw measurement arcs for each angle?8. Did I put my own personal flavor into the project?9. Is my project neat?10. Is my project beautiful?

This project is worth 50 points!