angles: naming, types, and how to measure them

ANGLES: NAMING, TYPES, AND HOW TO MEASURE

THEM

WHAT IS AN ANGLE?

An angle is defined as the amount of turn between two straight lines that share a common end point.  Angles are measured in degrees.  The symbol used for degrees is a

little circle °. 

Amount of turn

Microsoft Clip Art

Drawn by J. Bouchard

TERMS ASSOCIATED WITH ANGLES VERTEX - The vertex of an angle is the common point

where the two lines meet. ARM -  The arms of an angle or sides are the lines that

make up the angle. DEGREES - The size of the angle is measured in degrees

and usually denoted with the ° symbol.  For example, an angle may measure 45°.

PROTRACTOR - A tool that is used to measure angles.

ArmVertex 45°

Protractor

Arm

Microsoft Clip Art

NAMING ANGLES There are different ways to name angles.  One way is to

use the ∠ symbol followed by three letters.  From the diagram below you see ∠BAC.  The first and third letters indicate points on the two arms.  The letter in the middle is the vertex.  The first and third letters can be switched because they measure the same angle.  For example, ∠BAC is the same as ∠CAB. 

Drawn by J. Bouchard

NAMING ANGLES (continued)

Another way to label the angle is by using the ∠ symbol with the only the vertex point.  The angle would be called ∠A. 

Finally, the last way to label the angle would be by using the ∠ symbol followed by the letter or number between the angle.  This would be ∠x.  

Drawn by J. Bouchard

PRACTICE NAMING ANGLES Name all the possible angles shown below

1.

3.

2. Click for more PRACTICE

Pictures drawn by J. Bouchard

FOUR TYPES OF ANGLES

ACUTE

RIGHT

OBTUSE

STRAIGHTPhoto used under creative commons from Eric

ACUTE ANGLES

An acute angle is an angle that measures greater than 0° and less than 90°.

80°

30°

Microsoft Clip Art

RIGHT ANGLES

A right angle is an angle that measures 90°.

Photo used under creative commons from Camera Eye Photography

90°

OBTUSE ANGLES

An obtuse angle is an angle that measures greater than 90° and less than 180°.

Photo used under creative commons from Judy Baxter

115°

155°

STRAIGHT ANGLES

A Straight angle looks like a straight line and measures 180°. It is half a revolution of a circle.

Photo used under creative commons from Simon Harrod

180°

Can you identify the angles below?

1.

2.

3.

4.

5.

6.

Identify the type of angle from the measure shown below

1. 180° 4. 117°

2. 33° 5. 153°

3. 90° 6. 27°

Click here to practice Photo used under creative commons from Kevin Dooley

HOW TO USE A PROTRACTORA protractor has two scales: •The outer scale reads from 0° to 180° reading from left to right. •The inner scale reads from 0° to 180° reading from right to left.

Protractor picture taken from Clip Art etc. http://etc.usf.edu/clipart/

MEASURING ANGLESTo measure ∠ABC:1.Place the center of the

protractor on the vertex B.2.Adjust the 0° line or

baseline of the protractor so that it lines up with line BC.

3.Since the angle is acute and the 0° line or baseline was used from the right, you will take the reading from the inner scale.

Protractor picture taken from Clip Art etc. http://etc.usf.edu/clipart/

MEASURING ANGLES (CONTINUED)

If an angle is facing the other direction and the 0° line or baseline was used on the left, the outer scale will be used.  Since it is on the left and you know the angle is obtuse, reading from left to right the measurement is 100°.

Protractor picture taken from Clip Art etc. http://etc.usf.edu/clipart/

LET’S PRACTICE What is the measure of the angle below?

LET’S PRACTICE (continued)

What is the measure of the angle below?

LET’S PRACTICE (continued)

What is the measure of the angle below?

Click here for more practice

REFERENCES Slide 7: “From Every Angle” Photo used under creative commons

from Eric Slide 9: “Right Angle…Week #27” Photo used under creative

commons from Camera Eye Photography Slide 10: “Our Daily Challenge: ANGLES” Photo used under

creative commons from Judy Baxter Slide 11: “Tangential: M180” Photo used under creative commons

from Simon Harrod Slide 13: “48 angles” Photo used under creative commons from

Kevin Dooley