warm up draw each figure. 1. line segment 2. line 3. ray 4. plane
DESCRIPTION
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
Warm UpDraw each figure.
1. line segment
2. line
3. ray
4. plane
Course 2
7-2 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°
Course 2
7-2 Classifying Angles
Learn to identify angles and angle pairs.
Course 2
7-2 Classifying Angles
Vocabularyanglevertexright angleacute angleobtuse anglestraight anglecomplementary anglessupplementary angles
Insert Lesson Title Here
Course 2
7-2 Classifying Angles
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
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
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
Course 2
7-2 Classifying Angles
You can name this angle ABC, CBA, B, or 1.
Reading Math
A •
B • • C
1
Check It Out: Example 1
Insert Lesson Title Here
Tell whether each angle is acute, right, obtuse, or straight.
A. B.
straight angle acute angle
Course 2
7-2 Classifying Angles
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
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°.
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
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
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°.
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.
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°.
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.
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°.
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°.
Lesson Quiz: Part ITell whether each angle is acute, right, obtuse, or straight.
Insert Lesson Title Here
1. straight
obtuse
Course 2
7-2 Classifying Angles
2.
Lesson Quiz: Part IIUse the diagram to tell whether the angles are complementary, supplementary, or neither.
Insert Lesson Title Here
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°