This document defines angles and describes how to name, classify, and measure them. It discusses the key terms related to angles including vertex, arms, degrees, and protractor. There are four main types of angles: acute angles which are less than 90 degrees, right angles which are 90 degrees, obtuse angles which are greater than 90 degrees but less than 180 degrees, and straight angles which are 180 degrees. The document demonstrates how to use a protractor to accurately measure the degree of an angle.

1. ANGLES: NAMING, TYPES,
AND HOW TO MEASURE
THEM

2. 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

3. 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.
Arm
Vertex
45°
Protractor
Microsoft Clip Art

4. 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

5. 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

6. PRACTICE NAMING ANGLES
Name all the possible angles shown below
1.
3.
2.
Click for more PRACTICE
Pictures drawn by J. Bouchard

7. FOUR TYPES OF ANGLES
Photo used under creative commons from Eric

8. ACUTE ANGLES
An acute angle is an angle that measures
greater than 0° and less than 90°.
80°
30°
Microsoft Clip Art

9. RIGHT ANGLES
A right angle is an angle that measures
90°.
Photo used under creative commons from Camera Eye Photography
90°

10. 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°

11. 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°

12. Can you identify the angles below?
1.
2.
3.
4.
5.
6.

13. 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

14. HOW TO USE A PROTRACTOR
A 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/

15. MEASURING ANGLES
To 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/

16. 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/

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

18. LET’S PRACTICE (continued)
What is the measure of the angle below?

19. LET’S PRACTICE (continued)
What is the measure of the angle below?
Click here for more practice

20. 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