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8-2 Classifying Angles
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
8-2 Classifying Angles
Math Journal (5 Min)
• K-W-L - Each student will be given the title of the
lesson that will be taught that day. They must
then, at the beginning of class, write the “K” what
they know and “W” what they want to know
about the lesson before they have been taught
the lesson, and at the end of class, write the “L”
what they now know (Learned) about the lesson
after they have been taught the lesson. Then,
each student will discuss his/her answers within
their group. Finally, to leave class, each student
will have to give/write 1 sentence that they
learned that pertained to the lesson.
8-2 Classifying Angles
Homework Review (5 Min)
8-2 Classifying Angles
Warm Up
Draw each figure.
1. line segment
2. line
3. ray
4. plane
8-2 Classifying Angles
Problem of the Day
Find the measure of the smaller angle
between the hour and minute hands on
a clock at eight o’clock?
120°
8-2 Classifying Angles
Textbook Examples (I Do) (5 Min)
8-2 Classifying Angles
Learn to identify angles and angle pairs.
8-2 Classifying Angles
Vocabulary
angle
vertex
right angle
acute angle
obtuse angle
straight angle
complementary angles
supplementary angles
8-2 Classifying Angles
A
Vertex
An angle is formed by two
rays with a common
endpoint. The two rays are
the sides of the angle. The
common endpoint is the
vertex.
B
1
Angles are measured in degrees (°).
C
8-2 Classifying Angles
An angle’s measure determines the type of
angle it is.
A right angle is an angle that
that measures exactly 90°. The
symbol indicates a right angle.
An acute angle is an angle
that measures less than 90°.
An obtuse angle is an angle
that measures more than 90°
but less than 180°.
A straight angle is an angle
that measures exactly 180°.
8-2 Classifying Angles
Additional Example 1: Classifying Angles
Tell whether each angle is acute, right, obtuse
or straight.
A.
obtuse angle
B.
acute angle
8-2 Classifying Angles
Reading Math
A•
B•
1
•
C
You can name this angle ABC,
CBA, B, or 1.
8-2 Classifying Angles
Check It Out: Example 1
Tell whether each angle is acute, right,
obtuse, or straight.
A.
straight angle
B.
acute angle
8-2 Classifying Angles
If the sum of the measures of two angles is
90°, then the angles are complementary
angles. If the sum of the measures of two
angles is 180°, then the angles are
supplementary angles.
8-2 Classifying Angles
Additional Example 2A: Identifying Complementary
and Supplementary Angles
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
OMP and PMQ
To find mPMQ start with the measure that QM
crosses, 105°, and subtract the measure that MP
crosses, 75°. mPMQ = 105° - 75° = 30°. mOMP =
P
60°.
Q
Since 60° + 30° = 90°,
PMQ and OMP are
complementary.
O
N
M
R
8-2 Classifying Angles
Reading Math
If the angle you are measuring
appears obtuse, then its measure is
greater than 90°. If the angle is
acute, its measure is less than 90°.
8-2 Classifying Angles
Additional Example 2B: Identifying Complementary
and Supplementary Angles
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
NMO and OMR
mNMO = 15° and mOMR = 165°
P
Since 15° + 165° = 180°,
NMO and OMR are
supplementary.
Reading Math
Read mNMO as
“the measure of
angle NMO.”
Q
O
N
M
R
8-2 Classifying Angles
Additional Example 2C: Identifying Complementary
and Supplementary Angles
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
PMQ and QMR
To find mPMQ start with the measure that QM
crosses, 105°, and subtract the measure that MP
crosses, 75°. mPMQ = 105° - 75° = 30°. mQMR =
75°.
P
Q
Since 30° + 75° = 105°,
PMQ and QMR are
neither complementary
nor supplementary.
O
N
M
R
8-2 Classifying Angles
Check It Out: Example 2A
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
BAC and CAF
mBAC = 35° and mCAF = 145°
Since 35° + 145° = 180°,
BAC and CAF are
supplementary.
D
E
C
F
B
A
8-2 Classifying Angles
Check It Out: Example 2B
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
CAD and EAF
To find mCAD start with the measure that DA
crosses, 90°, and subtract the measure that CA
crosses, 35°. mCAD = 90° - 35° = 55°. mEAF =
D
35°.
Since 55° + 35° = 90°,
CAD and EAF are
complementary.
E
C
F
B
A
8-2 Classifying Angles
Check It Out: Example 2C
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
BAC and EAF
mBAC = 35° and mEAF = 35°
Since 35° + 35° = 70°,
BAC and EAF are
neither supplementary
nor complementary.
D
E
C
F
B
A
8-2 Classifying Angles
Additional Example 3: Finding Angle Measures
Angles A and B are complementary. If mA is
56°, what is the mB?
Since A and B are complementary, mA + mB =
90°.
mA + mB = 90°
56° + mB = 90°
– 56°
– 56°
mB = 34°
Substitute 56° for mA.
Subtract 56° from both
sides.
The measure of B = 34°.
8-2 Classifying Angles
Check It Out: Example 3
Angles P and Q are supplementary. If mP is
32°, what is the mQ?
Since P and Q are supplementary, mP + mQ
= 180°.
mP + mQ = 180°
32° + mQ = 180°
– 32°
– 32°
mQ = 148°
Substitute 32° for mP.
Subtract 32° from both
sides..
The measure of Q = 148°.
8-2 Classifying Angles
Class work Problems (We Do) (10 Min)
• Pg. 318-319 (1-9)
8-2 Classifying Angles
8-2 Classifying Angles
8-2 Classifying Angles
Small Group CW(Yall Do) (10 Min)
• Pg. 318-319 (10-26 EOE)
8-2 Classifying Angles
8-2 Classifying Angles
8-2 Classifying Angles
Homework (You Do) (10 Min)
• Pg. 318-319 (11, 15, 17, 19, 23 odd)
8-2 Classifying Angles
Math Journal (5 Min)
• K-W-L - Each student will be given the title of the
lesson that will be taught that day. They must
then, at the beginning of class, write the “K” what
they know and “W” what they want to know
about the lesson before they have been taught
the lesson, and at the end of class, write the “L”
what they now know (Learned) about the lesson
after they have been taught the lesson. Then,
each student will discuss his/her answers within
their group. Finally, to leave class, each student
will have to give/write 1 sentence that they
learned that pertained to the lesson.
8-2 Classifying Angles
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
8-2 Classifying Angles
Lesson Quiz: Part I
Tell whether each angle is acute, right,
obtuse, or straight.
1.
straight
2.
obtuse
8-2 Classifying Angles
Lesson Quiz: Part II
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
3. AZB and BZC
neither
4. BZC and CZD
complementary
5. Angles M and N are supplementary. If
mM is 117°, what is mN? 63°
8-2 Classifying Angles
Lesson Quiz for Student Response Systems
1. Identify the type of the given angle.
A. acute
B. obtuse
C. right
D. straight
8-2 Classifying Angles
Lesson Quiz for Student Response Systems
2. Identify the type of the given angle.
A. acute
B. obtuse
C. right
D. straight
8-2 Classifying Angles
Lesson Quiz for Student Response Systems
3. Use the diagram to identify the type of the given
pair of angles. mAOB and mBOD
A. complementary
B. supplementary
C. right
D. none
8-2 Classifying Angles
Lesson Quiz for Student Response Systems
4. Angles A and B are complementary. If mA is
36°, what is mB?
A. 54°
B. 90°
C. 126°
D. 144°