1.4
Angles and Their Measures
Objectives:
1. To name, classify, and measure angles.
2. Use the Angle Addition Postulate.
Key Vocabulary:
Angle



two rays with a common initial point.
the rays are called the sides of the angle.
the common initial point is called the vertex.
Naming Angles:
A is the vertex of
the angle
A
B
AB and AC are
the sides of the angle
3
the symbol for angle
BAC or A
is the name of the angle
C
angles can also be named
by a number placed in
the interior of the angle.
3
Example 1:
G
Name the indicated angle.
GDF or FDC
FDG
CDF
GDC
CDG
D
F
C
E
Key Vocabulary:
Angle Measurement
The number of degrees in an arc between
the sides of an angle.
mA
B
C
A
Measuring Angles:
Angle Measurement
A protractor is used to measure an angle.

line-up one side of the angle with a zero on the protractor.
A
Measuring Angles:
Angle Measurement
A protractor is used to measure an angle.

line-up one side of the angle with a zero on the protractor.
The vertex
always goes
A here
Measuring Angles:
Angle Measurement
A protractor is used to measure an angle.

line-up one side of the angle with a zero on the protractor.
A
A
Measuring Angles:
Angle Measurement
A protractor is used to measure an angle.
line-up one side of the angle with a zero on the protractor.
 follow the number of degrees
mA  102
up to the other side
of the angle.

A
Measuring Angles:
Angle Measurement
A protractor is used to measure an angle.

The same measure will result no matter which
side is on the zero.
mA  102
Key Vocabulary:
Congruent Angles
Angles that have the same measure
mA  mP
a number equal to a number
A  P
figures the same size and shape
Postulate
Angle Addition Postulate
If P is in the interior of CAB
then mCAP  mPAB  mCAB
C
P
A
B
Example 2:
In the figure mCDE  62 and mEDF  18.
Find mCDF .
D
C
mCDF  mCDE  mEDF
mCDF  62  18
mCDF  80
E
F
Practice 1:
In the figure mCDF  101 and mEDF  15.
Find mCDE.
D
C
mCDF  mCDE  mEDF
101  mCDE  15
15
 15
mCDE  86
E
F
Classifying Angles:
Acute Angles
Angles with a measure between 0o and 90o.
0  mA  90
A
Classifying Angles:
Right Angles
Angles with a measure of exactly 90o.
mA  90
A
Classifying Angles:
.
90  mA  180
Obtuse Angles
A
Angles with a measure between 90o and 180o.
Classifying Angles:
Straight Angles
Angles with a measure of exactly 180o.
mA  180
A
Example
Name an acute angle.
DEA
C
AEC
CEB
B
A
D
E
Example
Name a right angle.
DEC
C
B
A
D
E
Example
Name an obtuse angle.
DEB
AEB
C
B
A
D
E
Key Vocabulary:
Adjacent Angles (angles that are next to each other)
Two angles that have a common vertex and side,
but have no common interior points.
PR is the
common side
R
Q
QPR and RPS
are adjacent angles
S
P
common vertex
Example
Name a pair of adjacent angles.
DEA and AEC
C
DEA and AEB
B
A
AEC and CEB
DEC and CEB
D
E