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1.

UT

S

Angle at N: / or / Angle at T: / or /

2. Y

X

Z

3.

A

B

C

Angle at A: / or /

Angle at Y: / or / Angle at B: / or /

Angle at C: / or /

Name: Date:

Practice 1 Understanding and Measuring AnglesName the angles in two ways.

Angles

Cha

pter

Example

M

NP

Lesson 9.1 Understanding and Measuring Angles 45

MNP PNM

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Chapter 9 Angles

Name the marked angles in two ways.

E

D

CAB

p

rs

q

4. /q: / or /

5. /r: / or /

6. /s: / or /

Name the marked angles in two ways.

Q

R

aP

b

c

7. /PRQ: / or /

8. /QPR: / or /

/p: / or /

46

cExample/PQR: / or / RQP

ExampleDEAAED

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Name: Date:

Decide which scale you would use to measure each angle. Fill in the blanks with inner scale or outer scale.

100 110 120

130

140150

160170

180

8070

60

50

40

3020

100 0

1020

30

40

50

6070

80100110

120

130

140

150

160

170

180

100 110 120

130

140150

160170

180

8070

60

50

40

3020

100 0

1020

30

40

50

6070

80100110

120

130

140

150

160

170

180

9. 100 110 120

130

140150

160170

180

8070

60

50

40

3020

100 0

1020

30

40

50

6070

80100110

120

130

140

150

160

170

180

10. 100 110 120

130

140150

160170

180

8070

60

50

40

3020

100 0

1020

30

40

50

6070

80100110

120

130

140

150

160

170

180

11. 100 110 120

130

140150

160170

180

8070

60

50

40

3020

100 0

1020

30

40

50

6070

80100110

120

130

140

150

160

170

180

12.

100 110 120130

140150

160170

180

8070

60

50

40

3020

100 0

1020

30

40

50

6070

80100110

120

130

140

150

160

170

180

Lesson 9.1 Understanding and Measuring Angles 47

Examples

Outer scale Inner scale

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48 Chapter 9 Angles

13. 100 110 120

130

140150

160170

180

8070

60

50

40

3020

100 0

1020

30

40

50

6070

80100110

120

130

140

150

160

170

180

H G

I

Measure of /GHI 5

14. 100 110 120

130

140150

160170

180

8070

60

50

40

3020

100 0

1020

30

40

50

6070

80100110

120

130

140

150

160

170

180

K

L

J

Measure of /JKL 5

15.

100 110 120130

140150

160170

180

8070

60

50

40

3020

100 0

1020

30

40

50

6070

80100110

120

130

140

150

160

170

180

M

O

N

Measure of /MNO 5

Example100 110 120

130

140150

160170

180

8070

60

50

40

3020

100 0

1020

30

40

50

6070

80100110

120

130

140

150

160

170

180

E

F

D

Write the measure of each angle in degrees. State whether it is an acute angle or an obtuse angle.

Obtuse angle

137°Measure of /DEF 5

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a

Angle a b c d e f

Estimate

Measure

50°

60°

Estimate and then measure each angle.

16.

c

e

f

b

d

Name: Date:

Lesson 9.1 Understanding and Measuring Angles

Ask yourself, “Is the angle acute or obtuse?”

49

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50 Chapter 9 Angles

A

B

C

D

E

F

G

I

H

Example

Measure of �ABC 5

Measure of �GHI 5 Measure of �CDE 5

Measure of �DEF 5

Measure of �EFG 5

Measure of �FGH 5

Peter is walking along a path. Measure the marked angles along this path.

17.

120°

51

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Name: Date:

Practice 2 Drawing Angles to 180°Use a protractor to draw each angle.

1. 70° using inner scale 2. 147° using outer scale

100 110 120130

140150

160170

180

8070

60

50

40

3020

100 0

1020

30

40

50

6070

80100110

120

130

140

150

160

170

180

100 110 120130

140150

160170

180

8070

60

50

40

3020

100 0

1020

30

40

50

6070

80100110

120

130

140

150

160

170

180

3. 35° using inner scale 4. 108° using outer scale

100 110 120130

140150

160170

180

8070

60

50

40

3020

100 0

1020

30

40

50

6070

80100110

120

130

140

150

160

170

180

100 110 120130

140150

160170

180

8070

60

50

40

3020

100 0

1020

30

40

50

6070

80100110

120

130

140

150

160

170

180

Join the marked endpoint of each ray to one of the dots to form an angle with the given value. Then label the angle.

Measure of /p 5 105° 5. Measure of /h 5 32°

Example

p

Lesson 9.2 Drawing Angles to 180°

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52 Chapter 9 Angles

Join the marked endpoint of each ray to one of the dots to form an angle with the given value. Then label the angle.

6. Measure of /m 5 70° 7. Measure of /w 5 10°

Using point A as the vertex, draw /CAB as described.

80°, with AC above AB 8. 80°, with AC below AB

9. 130°, with AC above AB 10. 130°, with AC below AB

Example

A B

A

A

A

B

B

B

C

80°

53

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Use ray CD as one ray of an angle. Draw an angle with each given angle measure.Then state whether it is an acute angle, an obtuse angle, or a straight angle.

11. 160°

40°

Acute angle

12. 180° 13. 155°

Name: Date:

Example

Lesson 9.2 Drawing Angles to 180°

D

DD

C

C

D

C

CC

D

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54 Chapter 9 Angles

Draw an angle that has each measure.

14. 35°

15. 125°

55

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Lesson 9.2 Drawing Angles to 180°

Measure the angles in the triangles and redraw them in the boxes provided.

16. a. /ABC 5

/BAC 5

/ACB 5

b. /ABC 5

/BAC 5

/ACB 5

c. /ABC 5

/BAC 5

/ACB 5

A

B C

A B

C

B

A C

Name: Date:

57

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Lesson 9.1 Understanding Tenths

Practice 3 Turns and Right AnglesFind the measure of each angle.

1. 2.

A 12 -turn is . A 3

4 -turn is .

Fill in the blanks.

3. 4.

A -turn is 90°. A turn is 360°.

Lesson 9.3 Turn and Right Angles

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58 Chapter 9 Angles

Look at the three pairs of angle strips shown.

A B C

Which pair of angle strips shows:

5. 12 -turn? 6. a straight angle?

7. a turn between a 12 -turn and a 3

4 -turn?

Look at the three pairs of angle strips shown.

D E

F

Which pair of angle strips shows:

8. 360°?

9. an angle between 180° and 360°?

Complete.

10. 180° makes up of a full turn.

11. Three right angles make up a -turn.

12. 105° is between a -turn and a -turn.

Name: Date:

59

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13. Use a protractor to measure �XOY.

14. What fraction of the circle is the measure of �XOY?

90

O

100 110120

130

140150

160170

180190

200210

220

230240

250260270280290300310

320

330

340

350

010

2030

40

5060

7080

Y

X

Lesson 9.3 Turns and Right Angles

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60 Chapter 9 Angles

Example

m/STU 5 m/STV 1 m/VTU

5 25° 1 90°

5 115°

Find the measure of /STU.

15. Find the measure of /ABC.

25°

S

V

U

T

71°

AD

C

B98°36°

YX

W

Z

16. Find the measure of /XYZ.

17. The laptop was first opened to a measure of /AOB. Then it was increased by 80°. Find the measure of /COB.

50°

A

B

C

O

80°

Name: Date:

61

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18. Find the measure of �y. 19. The measure of �KLM is 152°. Find the measure of �a.

17°

Q

RO

P

y

28°a

L

MN

K

Example

m�x 5 m�DFG 2 m�EFG

5 180° 2 65°

5 115°

The measure of �EFG is 65°. DFG is a straight line. Find �x.

65°

GF

E

x

D

20. The clock shows the hands of the clock at a certain time. Find the measure of �z, if the measure of �MOP is 135°.

M

N

P

Oz

30°

Lesson 9.3 Turns and Right Angles

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62 Chapter 9 Angles

1. Which statements are wrong? Explain your answer.

a. Two right angles form a 12 -turn.

b. The measure of an angle is a fraction of a 34 -turn.

c. An acute angle has a measure greater than 90°.

d. A 14 -turn is 90°.

e. A straight angle has a measure of 180°.

f. 150° is between a 14 -turn and a 1

2 -turn.

g. A 120° angle is 13 of a full turn.

Name: Date:

62 Chapter 9 Angles

63

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Complete.

2. Conrad named the angle as shown. Is he correct? Explain your answer.

E

FG

The names of the angle are �EFG, �FGE, and �F.

f

Chapter 9 Angles

65

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Chapter 9 Angles

Put On Your Thinking Cap!

Challenging Practice

Look at the clock. The hour hand and minute hand were at the position as shown in figure A. Figure B shows the position of the hour hand and minute hand after some time.

What fraction of a turn did the minute hand move? Explain your answer.

A B

Name: Date:

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66 Chapter 9 Angles

Look at the diagram.

Tom walks from J to K and at that point makes a 14 -turn to his right.

Then, he walks to H and at that point, makes a 12 -turn before walking on

to the end of that line.

Where will he be?

Put On Your Thinking Cap!

Problem Solving

JK

B

C

D

E

FH

G

I

A