warm up draw each figure. 1. line segment 2. line 3. ray 4. plane
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7-2. Classifying Angles. Course 2. Warm Up Draw each figure. 1. line segment 2. line 3. ray 4. plane. 7-2. Classifying Angles. Course 2. 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°. 7-2. - PowerPoint PPT PresentationTRANSCRIPT
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Warm UpDraw each figure.
1. line segment
2. line
3. ray
4. plane
Course 2
7-2 Classifying Angles
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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°
Course 2
7-2 Classifying Angles
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Learn to identify angles and angle pairs.
Course 2
7-2 Classifying Angles
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Vocabularyanglevertexright angleacute angleobtuse anglestraight anglecomplementary anglessupplementary angles
Insert Lesson Title Here
Course 2
7-2 Classifying Angles
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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.
Angles are measured in degrees (°).
A
CB
1
Vertex
Course 2
7-2 Classifying Angles
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An angle’s measure determines the type of angle it is.
A right angle is an angle that that measures exactly 90°. Thesymbol indicates a right angle.An acute angle is an anglethat measures less than 90°.
An obtuse angle is an anglethat measures more than 90°but less than180°.
A straight angle is an anglethat measures 180°.
Course 2
7-2 Classifying Angles
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Tell whether each angle is acute, right, obtuse or straight.
Additional Example 1: Classifying Angles
A. B.
obtuse angle acute angle
Course 2
7-2 Classifying Angles
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Course 2
7-2 Classifying Angles
You can name this angle ABC, CBA, B, or 1.
Reading Math
A •
B • • C
1
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Check It Out: Example 1
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Tell whether each angle is acute, right, obtuse, or straight.
A. B.
straight angle acute angle
Course 2
7-2 Classifying Angles
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If the sum of the measures of two angles is90°, then the angles are complementary angles. If the sum of the measures of twoangles is 180°, then the angles are supplementary angles.
Course 2
7-2 Classifying Angles
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Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Additional Example 2A: Identifying Complementary and Supplementary Angles
Course 2
7-2 Classifying Angles
OMP and PMQ
Since 60° + 30° = 90°, PMQ and OMP are complementary. O
N
P Q
RM
To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° - 75° = 30°. mOMP = 60°.
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Course 2
7-2 Classifying Angles
If the angle you are measuring appears obtuse, then it measure is greater than 90°. If the angle is acute, its measure is less than 90°.
Reading Math
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Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Additional Example 2B: Identifying Complementary and Supplementary Angles
Course 2
7-2 Classifying Angles
NMO and OMR
mNMO = 15° and mOMR = 165°
O
N
P Q
RM
Since 15° + 165° = 180°, NMO and OMR are supplementary.
Read mNMO as “the measure of angle NMO.”
Reading Math
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Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Additional Example 2C: Identifying Complementary and Supplementary Angles
Course 2
7-2 Classifying Angles
PMQ and QMR
O
N
P Q
RM
Since 30° + 75° = 105°, PMQ and QMR are neither complementary nor supplementary.
To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° - 75° = 30°. mQMR = 75°.
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Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Check It Out: Example 2A
Course 2
7-2 Classifying Angles
BAC and CAF
mBAC = 35° and mCAF = 145°
C
B
D
E
FA
Since 35° + 145° = 180°, BAC and CAF are supplementary.
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Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Check It Out: Example 2B
Course 2
7-2 Classifying Angles
CAD and EAF
Since 55° + 35° = 90°, CAD and EAF are complementary.
C
B
D
E
FA
To find mCAD start with the measure that DA crosses, 90°, and subtract the measure that CA crosses, 35°. mCAD = 90° - 35° = 55°. mEAF = 35°.
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Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Check It Out: Example 2C
Course 2
8-2 Classifying Angles
BAC and EAF
mBAC = 35° and mEAF = 35°
C
B
D
E
FA
Since 35° + 35° = 70°, BAC and EAF are neither supplementary nor complementary.
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Angles A and B are complementary. If mA is 56°, what is the mB?
Additional Example 3: Finding Angle Measures
Since A and B are complementary, mA + mB = 90°.
Course 2
7-2 Classifying Angles
mA + mB = 90°
56° + mB = 90°
– 56° – 56°
mB = 34°
Substitute 56° for mA.
Subtract 56° from both sides to isolate mB.
The measure of B = 34°.
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Angles P and Q are supplementary. If mP is 32°, what is the mQ?
Check It Out: Example 3
Since P and Q are supplementary, mP + mQ = 180°.
Course 2
7-2 Classifying Angles
mP + mQ = 180°
32° + mQ = 180°
– 32° – 32°
mQ = 148°
Substitute 32° for mP.
Subtract 32° from both sides to isolate mQ.
The measure of Q = 148°.
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Lesson Quiz: Part ITell whether each angle is acute, right, obtuse, or straight.
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1. straight
obtuse
Course 2
7-2 Classifying Angles
2.
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Lesson Quiz: Part IIUse the diagram to tell whether the angles are complementary, supplementary, or neither.
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3. AZB and BZC neither
Course 2
7-2 Classifying Angles
4. BZC and CZD complementary
5. Angles M and N are supplementary. If M is 117°, what is mN? 63°