8-2 Classifying Angles

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpDraw each figure.

1. line segment

2. line

3. ray

4. plane

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°

Course 2

8-2 Classifying Angles

Learn to identify angles and angle pairs.

Course 2

8-2 Classifying Angles

Vocabularyanglevertexright angleacute angleobtuse anglestraight anglecomplementary anglessupplementary angles

Insert Lesson Title Here

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8-2 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

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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°. 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

8-2 Classifying Angles

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

Additional Example 1: Classifying Angles

A. B.

obtuse angle acute angle

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8-2 Classifying Angles

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8-2 Classifying Angles

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

Reading Math

A •

B • • C

1

Check It Out: Example 1

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

A. B.

straight angle acute angle

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8-2 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

8-2 Classifying Angles

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

Additional Example 2A: Identifying Complementary and Supplementary Angles

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8-2 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

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

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

Additional Example 2B: Identifying Complementary and Supplementary Angles

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8-2 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

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8-2 Classifying Angles

PMQ and QMR

O

N

P Q

RM

Since 30° + 75° = 105°, PMQ and QMR are neither complementary or 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

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8-2 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

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8-2 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

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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 or 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°.

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8-2 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 complementary, mP + mQ = 180°.

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8-2 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

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8-2 Classifying Angles

2.

Lesson Quiz: Part IIUse the diagram to tell whether the angles are complementary, supplementary, or neither.

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3. AZB and BZC neither

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8-2 Classifying Angles

4. BZC and CZD complementary

5. Angles M and N are supplementary. If M is 117°, what is mN? 63°