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# Warm Up - PowerPoint PPT Presentation

Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. Warm Up Draw each figure. 1. line segment 2. line 3. ray 4. plane. 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°.

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Presentation Transcript

Problem of the Day

Lesson Presentation

Lesson Quizzes

Draw each figure.

1. line segment

2. line

3. ray

4. plane

Find the measure of the smaller angle between the hour and minute hands on a clock at eight o’clock?

120°

Learn to identify angles and angle pairs.

angle

vertex

right angle

acute angle

obtuse angle

straight angle

complementary angles

supplementary angles

Vertex

1

B

C

An angleis 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 (°).

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°.

Anobtuse angle is an angle

that measures more than 90°

but less than 180°.

A straightangle is an angle

that measures exactly 180°.

Tell whether each angle is acute, right, obtuse or straight.

A.

B.

acute angle

obtuse angle

You can name this angle ABC, CBA, B, or 1.

A •

1

B•

•C

Tell whether each angle is acute, right, obtuse, or straight.

B.

A.

straight angle

acute angle

90°, then the angles are complementary

angles. If the sum of the measures of two

angles is 180°, then the angles are

supplementary angles.

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°.

P

Q

O

N

R

M

Additional Example 2A: Identifying Complementary and Supplementary Angles

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

OMP and PMQ

Since 60° + 30° = 90°, PMQ andOMP are complementary.

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°.

Q

O

Read mNMO as “the measure of angle NMO.”

N

R

M

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.

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

O

N

R

M

Additional Example 2C: Identifying Complementary and Supplementary Angles

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

PMQ and QMR

Since 30° + 75° = 105°, PMQ andQMR are neither complementary nor supplementary.

E

C

F

B

A

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.

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°.

D

E

C

F

B

A

Check It Out: Example 2B

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

Since 55° + 35° = 90°, CAD andEAF are complementary.

E

C

F

B

A

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.

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.

Subtract 56° from both sides.

– 56° – 56°

mB = 34°

The measure of B = 34°.

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°

Substitute 32° for mP.

Subtract 32° from both sides..

– 32°– 32°

mQ = 148°

The measure of Q = 148°.

Standard Lesson Quiz

Lesson Quiz for Student Response Systems

Lesson Quiz: Part I

Tell whether each angle is acute, right, obtuse, or straight.

straight

1.

obtuse

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

3. AZB and BZC

neither

complementary

4. BZC and CZD

5. Angles M and N are supplementary. If mM is 117°, what is mN?

63°

• 1. Identify the type of the given angle.

A. acute

B. obtuse

C. right

D. straight

• 2. Identify the type of the given angle.

A. acute

B. obtuse

C. right

D. straight

• 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

• 4. Angles A and B are complementary. If mA is 36°, what is mB?

A.54°

B.90°

C.126°

D.144°