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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 (°).

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°.

Anobtuse angle is an angle

that measures more than 90°

but less than 180°.

A straightangle is an angle

that measures exactly 180°.

Additional Example 1: Classifying Angles

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

A.

B.

acute angle

obtuse angle

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

B.

A.

straight angle

acute angle

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.

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°.

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 andOMP 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

Reading Math

O

Read mNMO 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

mNMO = 15° and mOMR = 165°

Since 15° + 165° = 180°, NMO andOMR are 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°.

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 andQMR 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

mBAC = 35° and mCAF = 145°

Since 35° + 145° = 180°, BAC andCAF are supplementary.

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°.

D

E

C

F

B

A

Check It Out: Example 2B

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

CAD and EAF

Since 55° + 35° = 90°, CAD andEAF 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

mBAC = 35° and mEAF = 35°

Since 35° + 35° = 70°, BAC andEAF are neither supplementary nor complementary.

Additional Example 3: Finding Angle Measures

Angles A and B are complementary. If mA is 56°, what is the mB?

Since A and B are complementary, mA + mB = 90°.

mA + mB = 90°

56° + mB = 90°

Substitute 56° for mA.

Subtract 56° from both sides.

– 56° – 56°

mB = 34°

The measure of B = 34°.

Angles P and Q are supplementary. If mP is 32°, what is the mQ?

Since P and Q are supplementary, mP + mQ = 180°.

mP + mQ = 180°

32° + mQ = 180°

Substitute 32° for mP.

Subtract 32° from both sides..

– 32°– 32°

mQ = 148°

The measure of Q = 148°.

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 mM is 117°, what is mN?

63°

Lesson Quiz for Student Response Systems

- 1. Identify the type of the given angle.
A. acute

B. obtuse

C. right

D. straight

Lesson Quiz for Student Response Systems

- 2. Identify the type of the given angle.
A. acute

B. obtuse

C. right

D. straight

Lesson Quiz for Student Response Systems

- 3. Use the diagram to identify the type of the given pair of angles. mAOB and mBOD
A. complementary

B. supplementary

C. right

D. none

Lesson Quiz for Student Response Systems

- 4. Angles A and B are complementary. If mA is 36°, what is mB?
A.54°

B.90°

C.126°

D.144°

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