Transcript Classifying Angles

8-2 Classifying Angles
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
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
I can 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°.