MEASURING AND NAMING ANGLES
LESSON 2-B
A
ngles are used in construction, architecture, graphic design, aerospace, art, machining and manufacturing,
as well as many other fields. An angle is formed by two rays with a common endpoint. A ray has one endpoint
and extends forever in one direction.
​___›
​__
​ A _›
(ra N
y N  ​ 
A)
The vertex of an angle is the common point of both rays. N is the vertex of
this angle.
N
When three points are used to name an angle, the vertex is written in the middle
of the name. The vertex can be written as the name of an angle when it is the
vertex for only one angle.
​__
​ _›
(ra N
y N G ​ 
G)
​___›
G
EXAMPLE 1
​___›
Ray NA is written NA​
​   . Ray NG is written NG​
​  . The first point in the name of a
ray is the endpoint.
A
​___›
Three ways to name the angle formed by NA​
​   and NG​
​   are ∠ANG, ∠GNA and ∠N.
Give 4 different names for the given angle.
P
1
A
L
Solution
EXAMPLE 2
1. ∠PAL
2. ∠LAP
3. ∠A
Is ∠W another name for ∠NWE? Explain.
E
N
Solution
4. ∠1
S
W
No, it is not clear whether ∠W refers to ∠NWE, ∠SWE or ∠NWS.
​___›
Adjacent angles are two angles that share a ray. In Example 2, ∠NWE and ∠SWE share WE​
​   .
This means ∠NWE and ∠SWE are adjacent angles.
6 Lesson 2-B ~ Measuring And Naming Angles
Identify at least one additional name for each angle. Write using proper
angle notation.
T
a. ∠1
EXAMPLE 3
I
b. ∠TGI 1
c. ∠RGE
Solutions
E
2
3
G
R
a. ∠TGE or ∠EGT
b. ∠2 or ∠IGT
c. ∠EGR or ∠3
A protractor is a tool used to measure angles. Angles are measured in units called degrees.
The “m” in front of an angle measure is notation for the word “measure”.
The statement in Figure 1 below reads, “The measure of ∠ABC is equal to sixty degrees.”
Figure 1
Figure 2
Figure 3
Z
A
P
60°
B
C
m∠ABC = 60°
Q
142°
R
X
m∠PQR = 142°
74°
Y
m∠ZYX = 74°
Lesson 2-B ~ Measuring And Naming Angles 7
Use a protractor to measure each angle.
C
a.b.
EXAMPLE 4
5
B
A
C
Solutions
a. b.
B
5
A
m∠ABC = 53°
m∠5 = 132°
EXERCISES
Give two different names for each angle.
1. 2. 3.
Q
L
B
P
U
J
K
A
Sketch a diagram to represent each angle.
4. ∠DOG 5. ∠CUB also called ∠4
6. ∠PAL also called ∠2 7. ∠1 and ∠2 are adjacent angles
8. ∠XYZ and ∠XYU are adjacent angles 9. ∠HOT is approximately 90°
Use each protractor to determine the measure of the angle.
10.11.
L
G
M
8 S
Lesson 2-B ~ Measuring And Naming Angles
B
I
T
Use a protractor to measure each angle to the nearest degree.
G
12.
13.14.
D
M
R
E
A
F
U
N
15.16.17.
1
P
3
I
V
Use a protractor to draw each angle. Label the angle(s).
18. m∠SAM = 34° 19. m∠YAK = 115° 20. m∠CAT = 167° 21. an 80° angle with PQ​
​   and PR​
​   
_​ __›
_​ __›
22. two 35° angles with the same vertex 23. two adjacent angles that are 50° and 100°
Use the diagram below to name an angle with the specified measure.
24. 90°25. 50°26. 17°
27. 145°28. 163°29. 130°
D
E
C
M
B
A
G
Lesson 2-B ~ Measuring And Naming Angles 9