Classifying Angles

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Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

Classifying Angles

Warm UpDraw each figure.

1. line segment

2. line

3. ray

4. plane

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°

Classifying Angles

Learn to identify angles and angle pairs.

Classifying Angles

Vocabularyanglevertexright angleacute angleobtuse anglestraight anglecomplementary anglessupplementary angles

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

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 than 180°.

A straight angle is an anglethat measures exactly 180°.

Classifying Angles

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

Additional Example 1: Classifying Angles

A. B.

obtuse angle acute angle

Classifying Angles

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

Reading Math

A •

B • • C

1

Classifying Angles

Check It Out: Example 1

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

A. B.

straight angle acute angle

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.

Classifying Angles

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

Additional Example 2A: Identifying Complementary and Supplementary 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°.

Classifying Angles

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°.

Reading Math

Classifying Angles

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

Additional Example 2B: Identifying Complementary and Supplementary 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

Classifying Angles

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

Additional Example 2C: Identifying Complementary and Supplementary 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°.

Classifying Angles

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

Check It Out: Example 2A

BAC and CAF

mBAC = 35° and mCAF = 145°

C

B

D

E

FA

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

Classifying Angles

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

Check It Out: Example 2B

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°.

Classifying Angles

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

Check It Out: Example 2C

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.

Classifying Angles

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°.

mA + mB = 90°

56° + mB = 90°

– 56° – 56°

mB = 34°

Substitute 56° for mA.

Subtract 56° from both sides.

The measure of B = 34°.

Classifying Angles

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°.

mP + mQ = 180°

32° + mQ = 180°

– 32° – 32°

mQ = 148°

Substitute 32° for mP.

Subtract 32° from both sides..

The measure of Q = 148°.

Classifying Angles

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Classifying Angles

Lesson Quiz: Part ITell whether each angle is acute, right, obtuse, or straight.

1. straight

obtuse2.

Classifying AnglesLesson 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 mM is 117°, what is mN? 63°

Classifying Angles

1. Identify the type of the given angle.

A. acute

B. obtuse

C. right

D. straight

Lesson Quiz for Student Response Systems

Classifying Angles

2. Identify the type of the given angle.

A. acute

B. obtuse

C. right

D. straight

Lesson Quiz for Student Response Systems

Classifying Angles

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

Classifying Angles

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

A. 54°

B. 90°

C. 126°

D. 144°

Lesson Quiz for Student Response Systems