1. 8-2 Classifying Angles Warm Up Problem of the Day Lesson Presentation
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. 8-2 Classifying Angles Warm Up Draw each figure. 1. line segment
Course 2
8-2
Classifying Angles
Warm Up
Draw each figure.
1. line segment
2. line
3. ray
4. plane

3. 8-2 Classifying Angles Problem of the Day
Course 2
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°

4. 8-2 Classifying Angles Learn to identify angles and angle pairs.
Course 2
8-2
Classifying Angles
Learn to identify angles and angle pairs.

5. Insert Lesson Title Here
Course 2
8-2
Classifying Angles
Insert Lesson Title Here
Vocabulary
angle
vertex
right angle
acute angle
obtuse angle
straight angle
complementary angles
supplementary angles

6. Course 2
8-2
Classifying Angles A C B 1
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.
Angles are measured in degrees (°).

7. 8-2 Classifying Angles An angle’s measure determines the type of
Course 2
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 than180°.
A straight angle is an angle
that measures 180°.

8. Additional Example 1: Classifying Angles
Course 2
8-2
Classifying Angles
Additional Example 1: Classifying Angles
Tell whether each angle is acute, right, obtuse or straight. A. B.
obtuse angle
acute angle

9. 8-2 Classifying Angles Reading Math
Course 2
8-2
Classifying Angles
You can name this angle ABC, CBA, B, or 1.
Reading Math
A •
B •
• C 1

10. Insert Lesson Title Here
Course 2
8-2
Classifying Angles
Insert Lesson Title Here
Check It Out: Example 1
Tell whether each angle is acute, right, obtuse, or straight. B. A.
straight angle
acute angle

11. 8-2 Classifying Angles If the sum of the measures of two angles is
Course 2
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.

12. Course 2
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 = 60°. O N P Q R M
Since 60° + 30° = 90°, PMQ and OMP are complementary.

13. 8-2 Classifying Angles Reading Math
Course 2
8-2
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

14. Course 2
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°
Since 15° + 165° = 180°, NMO and OMR are supplementary. O N P Q R M
Read mNMO as “the measure of angle NMO.”
Reading Math

15. Course 2
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°. O N P Q R M
Since 30° + 75° = 105°, PMQ and QMR are neither complementary or supplementary.

16. 8-2 Classifying Angles Check It Out: Example 2A
Course 2
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. C B D E F A

17. 8-2 Classifying Angles Check It Out: Example 2B
Course 2
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 = 35°. C B D E F A
Since 55° + 35° = 90°, CAD and EAF are complementary.

18. 8-2 Classifying Angles Check It Out: Example 2C
Course 2
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 or complementary. C B D E F A

19. Additional Example 3: Finding Angle Measures
Course 2
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°
Substitute 56° for mA.
– 56° – 56°
Subtract 56° from both sides to isolate mB.
mB = 34°
The measure of B = 34°.

20. 8-2 Classifying Angles Check It Out: Example 3
Course 2
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 complementary, mP + mQ = 180°.
mP + mQ = 180°
32° + mQ = 180°
Substitute 32° for mP.
– 32° – 32°
Subtract 32° from both sides to isolate mQ.
mQ = 148°
The measure of Q = 148°.

21. Insert Lesson Title Here
Course 2
8-2
Classifying Angles
Insert Lesson Title Here
Lesson Quiz: Part I
Tell whether each angle is acute, right, obtuse, or straight. 1.
straight 2.
obtuse

22. Insert Lesson Title Here
Course 2
8-2
Classifying Angles
Insert Lesson Title Here
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 is 117°, what is mN?
63°