3.2 Angle Measures
In this section we will:
1) Measure and estimate the measure of angles
2) Classify angles by their measure
3) Solve to find the value of x using angle measurements
1) Measure and estimate the measure of angles
We use the unit degrees to measure an angle
Postulate 3‐1
P
For every angle, there is a unique
positive number between 0 and 180
that is the degree measure of the
angle.
75o
Q
R
m
PQR = 75
Use a protractor to measure an angle.
D
E
F
W
Y
X
1
Estimating the measure of an angle
Always estimate to the nearest 10 or 5 (i.e. 25, 40, 155)
2
Ex 1) Find the measures of
BXE,
CXE,
AXB
C
B
A
E
X
Postuate 3‐2
For XB, an angle can be formed above or below the ray.
A
B
X
C
Ex 3) Use a protractor to draw an angle having a measure of 135o
Use a protractor to draw an angle having a measure of 57o
3
2) Classify angles by their measure
Types of Angles
A
Q
B
C
X
R
S
Y
Z
m ABC = 90
m QRS < 90
m XYZ > 90
Right Angle
Acute Angle
Obtuse Angle
Ex 4) Classify each angle as right, acute, or obtuse
110o
90o
40o
50o
130o
75o
4
3) Solve to find the value of x using angle measurements
Ex 5) The measure of angle B is 138. Solve for x.
5x ‐ 7
B
The measure of LDOG is 65o. Find the value of x.
D
(2x + 5)o
O
G
5