Reteach - Amphitheater Public Schools

Name ________________________________________ Date __________________ Class__________________

LESSON

1-3

Reteach

Measuring and Constructing Angles

An angle is a figure made up of two rays, or sides, that have a common endpoint,

called the vertex of the angle.

There are four ways to name this angle.

¡ÏY

Use the vertex.

¡ÏXYZ or ¡ÏZYX

Use the vertex and a point on each side.

¡Ï2

Use the number.

Name each angle in three ways.

1.

2.

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3. Name three different angles in the figure.

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Angle

acute

right

obtuse

straight

0¡ã < a¡ã < 90¡ã

a¡ã = 90¡ã

90¡ã < a¡ã < 180¡ã

a¡ã = 180¡ã

Model

Possible

Measures

Classify each angle as acute, right, obtuse, or straight.

4. ¡ÏNMP

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5. ¡ÏQMN

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6. ¡ÏPMQ

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1-22

Holt McDougal Geometry

Name ________________________________________ Date __________________ Class__________________

LESSON

1-3

Reteach

Measuring and Constructing Angles continued

You can use a protractor to

find the measure of an angle.

¡ÏGEF is obtuse.

¡ÏDEG is acute.

Use the figure above to find the measure of each angle.

7. ¡ÏDEG

8. ¡ÏGEF

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The measure of ¡ÏXVU can be found by adding.

m¡ÏXVU = m¡ÏXVW + m¡ÏWVU

= 48¡ã + 48¡ã

= 96¡ã

Angles are congruent if their measures areJJJJ

equal.

In the figure, ¡ÏXVW ? ¡ÏWVU

G

because the angles have equal measures. VW is an angle bisector of ¡ÏXVU because

it divides ¡ÏXVU into two congruent angles.

Find each angle measure.

9. m¡ÏCFB if ¡ÏAFC is a straight angle.

10. m¡ÏEFA if the angle is congruent

to ¡ÏDFE.

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11. m¡ÏEFC if ¡ÏDFC ? ¡ÏAFB.

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JJJG

12. m¡ÏCFG if FG is an angle bisector

of ¡ÏCFB.

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________________________________________

Original content Copyright ? by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

1-23

Holt McDougal Geometry

9. obtuse

6.

11. right

10. straight

12. acute

13. Check students¡¯ drawings.

14. Check students¡¯ drawings.

7. 7.5 < x < 22.5

8. back 2

15. Check students¡¯ drawings.

1

1

somersault 2 twists

2

2

16. Check students¡¯ drawings.

9. 68¡ã

1-4 PAIRS OF ANGLES

?¡ú

10. No, WZ does not have to be the angle

bisector of ¡ÏXWY.

Practice A

1. vertex; side

2. linear pair

3. 90¡ã

4. right angle

1. ¡ÏQ, ¡ÏPQR, ¡Ï1

5. Supplementary

6. straight angle

2. ¡ÏJ, ¡ÏHJK, ¡ÏKJH

7.

Reteach

3. ¡ÏABD, ¡ÏABC, ¡ÏDBC

4. obtuse

5. right

6. acute

7. 55¡ã

8. 125¡ã

9. 102¡ã

10. 51¡ã

8.

11. 129¡ã

12. 51¡ã

Challenge

9. 120¡ã

1.

10. 30.

11.

2. angle bisector

Practice B

3. It is double the number of cuts.

4. 360 ¡Â (2n) or 180 ¡Â n

1. 180¡ã

JJJG

2. QR

5. 20; 18¡ã

3. 137.9¡ã

4. (110 ? 8x)¡ã

5. 132¡ã

6. 135¡ã

Problem Solving

1. Sample answer: ¡ÏLKG, ¡ÏGKH, ¡ÏHKJ,

¡ÏJKL, ¡ÏLKH

7. m¡ÏDEF = 29¡ã; m¡ÏFEG = 61¡ã

2. 103¡ã

3. 100¡ã

4. 65¡ã

5. 27¡ã

9. Possible answers: ¡Ï1 and ¡Ï3 or ¡Ï2 and

¡Ï4

6. A

7. J

8. m¡ÏDEF = 91¡ã; m¡ÏFEG = 89¡ã

10. Possible answers: ¡Ï1 and ¡Ï2; ¡Ï2 and

¡Ï3; ¡Ï3 and ¡Ï4; or ¡Ï1 and ¡Ï4

Reading Strategies

1. obtuse

2. acute

3. right

4. right

5. straight

6. obtuse

7. acute

8. obtuse

11. right

12. 45¡ã; 45¡ã

Original content Copyright ? by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

A4

Holt McDougal Geometry

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