Sec 3.1

Angles & Angle Measurements

Classify angles as acute, obtuse, right, or straight.

Measure/Draw angles by using a protractor.

Objective: What we’ll learn…

What is an angle?

Two rays that share the same endpoint form an angle. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle.

Here are some examplesof angles.

Naming an Angle

We can identify an angle by using a point on each ray and the vertex. The angle below may be identified as angle ABC or as angle CBA; you may also see this written as < ABC or as < CBA. The vertex point is always in the middle.

(VERTEX)

(Ray)

(Ray)

Degrees: Measuring Angles

We measure the size of an angle using degrees. Example: Here are some examples of angles and their degree measurements.

ProtractorA device used to measure angles.

Reading a ProtractorDate: 9/8/96 at 22:29:58 From: Bob Vanselow Subject: Reading a Protractor Which side of a protractor scale do you use?

Date: 9/9/96 at 11:39:23 From: Doctor Robert Subject: Re: Reading a Protractor I think that the easiest way to decide which scale to use is to look at the angle you're measuring. If it is greater than a right angle (more than ninety degrees) then use the scale that has numbers greater than 90. If the angle is obviously acute (measures less than 90 degrees), use the scale which has numbersless than 90. Of course you have to line up the protractor correctly with the center point on the vertex of the angle and one of the rays of the anglecoincide with the line on the protractor. Happy measuring! -Doctor Robert, The Math Forum Check out our web site! http://mathforum.org/dr.math/

Acute Angles

An acute angle is an angle measuring between 0 and 90 degrees.

Example:

                                                             

  

Acute Angles

An acute angle is an angle measuring between 0 and 90 degrees.

Task:Draw the following acute angles in your notes.1) 72o 2) 60o 3) 51.5o

4) 45o 5) 40o 6) 36o

                                                               

Obtuse Angles

An obtuse angle is an angle measuring between 90 and 180 degrees.

Example:

                                                              

   

Obtuse Angles

An obtuse angle is an angle measuring between 90 and 180 degrees.

Task:Draw the following obtuse angles in your notes.1) 120o 2) 150o 3) 135o

4) 170o 5) 100o 6) 95o

                                                              

   

Right AnglesA right angle is an angle measuring 90 degrees.

Examples:

                                      

Straight AnglesA straight angle is an angle measuring 180 degrees.

Examples:

                                      

Review

State whether the following are acute, right, or obtuse.1.

2.

3.

4.

5.

??

acute obtuseright

obtuseacute

Sec 3.2

Angles & Angle Relationships

Complementary AnglesTwo angles are called complementary angles if the sum of their degree measurements equals 90 degrees.

Example:

These two angles are complementary.

                                                      

                        

These two angles can be "pasted" together to form a right angle!

                        

Supplementary AnglesTwo angles are called supplementary angles if the sumof their degree measurements equals 180 degrees.

Example:

These two angles are supplementary.

                                                                      

These two angles can be "pasted" together to form a straight line!

                                                

two angles…1)share a vertex 2)are directly across from each other3)created by two crossing lines.

Vertical Angles

Vertical Angles are congruent.

1 12

2

Vertical Angles

For any two lines that meet, such as in the diagram below, AEB and DEC are called vertical angles. BEC and AED are also vertical angles. Vertical angles have the same degree measurement.                                    

Linear Pair

Two angles…1)share a vertex 2)form a straight line (add to 180° or supplementary)3)must be ADJACENT (next to each other)

Complementary and Supplementary

1. Two angles are complementary. One measures 65 degrees.

2. Two angles are supplementary. One measures 140 degrees.

Find the missing angle.

Answer : 25

Answer : 40

Complementary and Supplementary

Find the missing angle. You do not have a protractor.Use the clues in the pictures.

1.2.x

55 165x

X=35 X=15

Vertical Angles

Find the missing angle. You do not have a protractor.

Use the clues in the pictures.

58x

X=58

More drawings

20

C

J

D

E F

G

H

70

9070

20

90

Final Drawing

52

B

A

F E

D

C

60

G

68

686052