Practice 1 Understanding and Measuring Angles Angles

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© M arshal l Ca vendish Int erna tional (Singapor e) Priv at e Limit ed. 1. U T 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 /

Practice 1 Understanding and Measuring Angles

Name the angles in two ways.

Angles

C

h

a p

t

er Example M N P

Lesson 9.1 UnderstandingandMeasuring Angles 45

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Name the marked angles in two ways.

E D C A B p r s q 4. /q: / or / 5. /r: / or / 6. /s: / or /

Name the marked angles in two ways.

Q R a P b c 7. /PRQ: / or / 8. /QPR: / or / /p: / or /

c

Example /PQR: / or /

RQP

Example

DEA

AED

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

100 110 120 130 140 150 160 17 0 18 0 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 100 110 120 130 140 150 160 170 18 0 100 11₀ 12₀ 130 140 150 160 17 0 18 0 80 70 60 50 40 30 20 10 0 0 1₀ 20 30 40 50 60 70 80 100 110 120 130 140 150 160 170 18 0 9. ₁₀₀ 110 120 130 140 150 160 170 1 80 80 70 60 50 40 30 20 10 0 0 1₀ 20 30 40 50 60 70 80 100 110 120 130 140 150 160 170 180 10. 100 110 120 130 140 150 160 17 0 180 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 100 110 120 130 140 150 160 170 18 0 11. 100 110 120 130 140 150 160 170 1 80 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 100 110 120 130 140 150 160 170 18 0 12. 100 110 120 130 140 150 160 170 1 80 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 100 110 120 130 140 150 160 170 18 0

Lesson 9.1 UnderstandingandMeasuring Angles 47

Examples

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© M arshal l Ca vendish Int erna tional (Singapor e) Priv at e Limit ed. 13. ₁₀₀ 110 120 130 140 150 160 170 180 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 100 110 120 130 140 150 160 170 180 H G I Measure of /GHI 5 14. ₁₀₀ 110₁₂₀ 130 140 150 160 170 180 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 100 110 120 130 140 150 160 170 180 K L J Measure of /JKL 5 15. 100 110₁₂₀ 130 140 150 160 170 180 80 70 60 50 40 30 20 10 0 0 10 2₀ 30 40 50 60 70 80 100 110 120 130 140 150 160 170 180 M O N Measure of /MNO 5 Example 100 110₁₂₀ 130 140 150 160 170 180 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 100 110 120 130 140 150 160 170 180 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°

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50°

60°

Estimate and then measure each angle. 16. c e f b d

Lesson 9.1 UnderstandingandMeasuring Angles

Ask yourself,

“Is the angle acute or obtuse?”

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© M arshal l Ca vendish Int erna tional (Singapor e) Priv at e Limit ed. 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.

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51 © M arshal l Ca vendish Int erna tional (Singapor e) Priv at e Limit ed.

Practice 2 Drawing Angles to 180°

Use a protractor to draw each angle.

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

100 110 ₁₂₀ 130 140 150 160 170 180 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 100 110 120 130 140 150 160 170 180 100 110₁₂₀ 130 140 150 160 170 180 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 100 110 120 130 140 150 160 17 0 180

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

100 110 ₁₂₀ 130 140 150 160 170 180 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 100 110 120 130 140 150 160 170 180 100 110₁₂₀ 130 140 150 160 170 180 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 100 110 120 130 140 150 160 17 0 180

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 /h5 32° Example

p

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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 ACabove AB 8. 80°, with AC below AB

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

Example A B A A A B B B

C

80°

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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° Example Lesson9.2 DrawingAngles to 180° D D D C C D C C C D

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Draw an angle that has each measure.

14. 35°

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55 © M arshal l Ca vendish Int erna tional (Singapor e) Priv at e Limit ed. Lesson9.2 DrawingAngles 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

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57 © M arshal l Ca vendish Int erna tional (Singapor e) Priv at e Limit ed. Lesson 9.1 Understanding Tenths Find the measure of each angle.

1. 2.

A 1₂ -turn is . A 3₄ -turn is .

Fill in the blanks.

3. 4.

A -turn is 90°. A turn is 360°.

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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 1

2 -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.

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

90 O 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 0 10 20 30 40 50 60 70 80 Y X Lesson 9.3 Turns and Right Angles

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Find the measure of /STU.

15. Find the measure of /ABC. 25° S V U T 71° A D C B 98° 36° Y X 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:

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

17° Q R O P y 28° a L M N K 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° G F 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 O z 30° Lesson 9.3 Turns and Right Angles

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1. Which statements are wrong? Explain your answer.

a. Two right angles form a 1

2 -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 1₂ -turn.

g. A 120° angle is 1₃ of a full turn.

Name: Date:

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

E

F G

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

f

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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.

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Look at the diagram.

Tom walks from J to K and at that point makes a 1

4 -turn to his right.

Then, he walks to H and at that point, makes a 1

2 -turn before walking on

to the end of that line. Where will he be?

Put On Your Thinking Cap!

Problem Solving

J K B C D E F H G I A