Transcript 1.4: Angle Measure

1.4: Angle Measure
SOL: G4
Objectives:
• Measure and classify angles.
• Identify special angle pairs.
• Use the special angle pairs to find angle measures.
Angle

formed by two noncollinear rays that
have a common endpoint.
B
A
C
Sides of an Angle

The rays that make the angle
Vertex of an Angle

The common endpoint
Side AB
Vertex A
B
A
Side AC
C
Symbols


When we name an angle, the vertex point
is always in the middle
The following are the different ways we
can name this angle:
B
A, BAC, CAB, 4
A
Note the vertex is the middle point listed
4
C
Interior of an Angle
 Any
point inside the angle
Exterior of an Angle
 Any
point outside the angle
Exterior
Interior
Exterior
Example 1:
Use the diagram to answer a, b, and c.
a.) Name all angles that have B as a vertex.
∡ABG, ∡ABD, ∡DBE or ∡DBF,
∡EBG or ∡FBG, ∡5, ∡6, ∡7
b.) Name the sides of 5.
BG and BE or BF
c.) Write another name for 6.
∡DBE or ∡DBF
Measuring Angles
To measure an angle, you use a protractor.
The protractor has two scales
running from 0 to 180 degrees
in opposite directions. These are
the scales we use to determine the
measure of the angle
Align the 0 on either side
of the scale with one side
of the angle. (Paying
attention to which
direction the angle is opening
Place the center point of the
protractor on the vertex
Example 2:
Find the measure of PQR.
R
65°
P
Q
Since QP is aligned with the 0
on the outer scale, use the outer
scale to find that QR intersects
the scale at 65 degrees.
Classify Angles by Angle Measure
Right Angle


Measures 90
Written as mA = 90
Acute Angle


Measures less than
90
Written as mB < 90
This symbol
means, right
angle,
perpendicular
A
B
Classify Angles by Angle Measure
Obtuse Angle


Measures greater than
90
Straight Angle
(Line)

Measures 180
Written as mC > 90
A
C
B
C
Example 3:
Measure the angle and classify it.
12°, Acute
Example 4:
Measure the angle and classify it.
99°, Acute
Example 5:
Measure the angle and classify it.
69°, Acute
Congruent Angles

Angles that have the same measure

Symbols: NMP  QMR
Postulate 1.8: Angle Addition Postulate

If point B is in the interior of ∠AOC , then
m∠AOB + m∠BOC = m∠AOC
Example 6:
23°
46°
M
If m∠EFG = 23°,
what is the m∠EFH? 12°
m∡EFG - m∡GFH = m∡EFH
D
A
Apply the angle addition postulate.
C
23° - 11° = 12°
K
68°
L
H
B
What is the
m∡ABC? 69°
m∡ABD + m∡CBD =
m∡ABC
23° + 46° = 69°
J
E
11° G
If m∠KJL = 117°,
what is the m∠KJM?
49°
F
m∡KJL - m∡LJM =
m∡KJM
117° - 68° = 49°
Example 7:
If m∠RQT = 155°, what are the
m∠RQS and m∠SQT?
m∡RQS + m∡TQS = m∡RQT
(4x – 20) + (3x + 14) = 155°
Check:
72° + 83° = 155°
7x – 6= 155°
+6
+6
7x = 161°
7x = 161°
7
7
x = 23°
m∡RQS = 4x – 20 = 4(23) – 20 = 72°
m∡TQS = 3x + 14 = 3(23) + 14 = 83°
Example 8: ∠DEF is a straight angle.
What are
the m∠DEC and m∠CEF?
m∡DEC + m∡FEC = m∡DEF
(11x – 12) + (2x + 10) = 180°
13x – 2 = 180°
+2
+2
13x = 182°
13x = 182°
13
13
x = 14°
m∡DEC = 11x – 12 = 11(14) – 12 = 142°
m∡FEC = 2x + 10 = 2(14) + 10 = 38°
Check:
142° + 38° = 180°