LESSON Practice B Measuring and Constructing Angles

Name

LESSON

1-3

Date

Class

Practice B

Measuring and Constructing Angles

Draw your answer on the figure.

1. Use a compass and straightedge

to

___?

construct angle bisector DG .

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'

&

$

#

2. Name eight different angles in the figure.

?A, ?C, ?ABC, ?ABD, ?ADB,

"

?ADC, ?CBD, and ?CDB

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Find the measure of each angle

and classify each as acute,

right, obtuse, or straight.

:

7

3. ?YWZ

4. ?XWZ

90; right

5. ?YWX

120; obtuse

30; acute

T is in the interior of ?PQR . Find each of the following.

6. m?PQT if m?PQR  25¡ã and m?RQT  11.

14

7. m?PQR if m?PQR  (10x  7), m?RQT  5x ¡ã, and m?PQT  (4x  6).

123

__?

8. m?PQR if QT bisects ?PQR, m?RQT  (10x  13), and m?PQT  (6x  1).

9. Longitude is a measurement of position around the equator of

Earth. Longitude is measured in degrees, minutes, and seconds.

Each degree contains 60 minutes, and each minute contains

60 seconds. Minutes are indicated by the symbol  and seconds

are indicated by the symbol . Williamsburg, VA, is located at

76¡ã4225. Roanoke, VA, is located at 79¡ã5730. Find the

difference of their longitudes in degrees, minutes, and seconds.

10. To convert minutes and seconds into decimal parts of a degree,

divide the number of minutes by 60 and the number of seconds

by 3,600. Then add the numbers together. Write the location of

Roanoke, VA, as a decimal to the nearest thousandths of a degree.

Copyright ? by Holt, Rinehart and Winston.

All rights reserved.

20

44

31505

79.958

Holt Geometry

Name

LESSON

1-3

Date

Class

Name

Practice A

LESSON

1-3

Measuring and Constructing Angles

Use the figure for Exercises 1¨C 4.

vertex

Practice B

Measuring and Constructing Angles

1. Use a compass and straightedge

to

___?

construct angle bisector DG .

?

.

?

?

?

2. Name the two rays that form ?P.

___?

___?

?

PQ and PR

?A, ?C, ?ABC, ?ABD, ?ADB,

?

?ADC, ?CBD, and ?CDB

4. Name a point that is in the interior of ?P.

.

4. ?XWZ

90?; right

8. ?DEA

180?; straight

60?; acute

??? ??

?

?? ?? ???

?? ???

??

?

?

3. ?YWZ

7. ?AEB

??

?

?

?

??

??

?? ??? ???

?? ???

?

??

?

?? ??

?

??? ??

?? ? ?

??

?

??

?

?? ??

?

??? ??

?? ? ?

??

?

??

?

protractor

Find the measure of each angle. Then tell whether

each is acute, right, obtuse, or straight.

?

???

???

??

???

? ?? ??

??

??

5. A tool used to measure and draw angles

??? ??

?

?? ?? ???

?? ???

??

??

???

???

??

???

? ?? ??

??

??

??

??

?? ??? ???

?? ???

?

??

?

Find the measure of each angle

and classify each as acute,

right, obtuse, or straight.

?

Complete the statement.

?

?

point S

90?; right

?

2. Name eight different angles in the figure.

?QPR and ?RPQ

6. ?CEA

?

?

?

?

3. Use the angle symbol and three letters to name ?P in two ways.

is called a

Class

Draw your answer on the figure.

1. An angle is a figure formed by two rays with a common

endpoint called the

Date

5. ?YWX

30?; acute

120?; obtuse

T is in the interior of ?PQR . Find each of the following.

Complete the angle.

14?

6. m?PQT if m?PQR ? 25¡ã and m?RQT ? 11?.

9. Use a compass and straightedge to finish constructing ?IHJ congruent to ?MLN.

7. m?PQR if m?PQR ? (10x ? 7)?, m?RQT ? 5x ¡ã, and m?PQT ? (4x ? 6)?.

123?

__?

?

?

?

8. m?PQR if QT bisects ?PQR, m?RQT ? (10x ? 13)?, and m?PQT ? (6x ? 1)?.

?

?

?

?

?

10. Marc doesn¡¯t think that the angle of the front seat

in his mom¡¯s car is very cool, so he tilts the seat

back. m?ZWY ? 95? and m?YWX ? 30?.

Find m?ZWX.

9. Longitude is a measurement of position around the equator of

Earth. Longitude is measured in degrees, minutes, and seconds.

Each degree contains 60 minutes, and each minute contains

60 seconds. Minutes are indicated by the symbol ? and seconds

are indicated by the symbol ?. Williamsburg, VA, is located at

76¡ã42?25?. Roanoke, VA, is located at 79¡ã57?30?. Find the

difference of their longitudes in degrees, minutes, and seconds.

?

?

?

19

Copyright ? by Holt, Rinehart and Winston.

All rights reserved.

Name

LESSON

1-3

?

Date

Class

Name

LESSON

1-3

?? ??

?

??? ??

?? ? ?

??

?

??

?

?

??? ??

?

?? ?? ???

?? ???

??

?

The vertex is Y.

?

a straight angle

Name each angle in three ways.

5. Describe how Keisha can draw an exact 45? angle using only a

straightedge and a compass.

?

First, Keisha can draw a straight angle (180¡ã). She can then bisect

?

?

?Q, ?PQR, ?1

__?

__?

Angle

7.5 ? x ? 22.5

3.6

Possible

Measures

3.6

3.7

right

obtuse

straight

0? ? a? ? 90?

??

??

a? ? 90?

90? ? a? ? 180?

a? ? 180?

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

3.8

4. ?NMP

obtuse

?

?

5. ?QMN

68¡ã

right

___?

?

?

10. m?XWY

___ is twice m?XWZ. Tell if WZ must be the angle bisector of ?XWY.

6. ?PMQ

?

No, WZ does not have to be the angle bisector of ?XWY.

Copyright ? by Holt, Rinehart and Winston.

All rights reserved.

?

??

??

back 2 _1_ somersault 2 _1_ twists

2

2

21

acute

?

Model

Difficulty

1 somersault

Back 3 _

2

1 somersault 1 twist

Forward 3 _

2

1 somersault 4 _

1 twists

Reverse 1 _

2

2

1 somersault 2 _

1 twists

Back 2 _

2

2

9. HJ bisects ?IHL, HK bisects ?JHL , and m?IHK ? 51?. Find m?IHL.

Copyright ? by Holt, Rinehart and Winston.

All rights reserved.

?

?

?ABD, ?ABC, ?DBC

????

8. In diving, a somersault is a full forward

rotation, and a twist is a full turn. The chart

names some of the most difficult platform

dives according to the International

Swimming Federation. Name the dive in

which the diver moves through a total of

exactly 1,800?.

?J, ?HJK, ?KJH

3. Name three different angles in the figure.

Dive

?

?

?

bisect one of the right angles to make a 45¡ã angle.

7. An acute angle measures (6x ? 45)?. Write an inequality to

describe the range of all possible values of x.

?

2.

1.

the straight angle to make two right angles (90¡ã). Keisha can then

Use the chart to complete the exercise.

The

__? sides

__?are

YX and YZ.

?

There are four ways to name this angle.

?Y

Use the vertex.

?XYZ or ?ZYX

Use the vertex and a point on each side.

?2

Use the number.

4. What kind of angle can Keisha draw exactly with only a straightedge?

6. Construct a 135? angle using only

a straightedge and a compass.

?

?

Keisha has a straightedge and a compass, but no protractor.

Draw your answer in the space provided.

Holt Geometry

Measuring and Constructing Angles

?

???

???

??

???

? ?? ??

??

?BAC, ?DAE,

?CAD

?BAD

and ?CAE

Name two right angles.

2. Name two acute angles.

??

Class

Reteach

??

??

??

?? ??? ???

?? ???

?

??

?

Date

79.958?

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

called the vertex of the angle.

?

?BAE

20

Copyright ? by Holt, Rinehart and Winston.

All rights reserved.

Measuring and Constructing Angles

1. Name the obtuse angle.

3.

Holt Geometry

Practice C

Use the figure for Exercises 1¨C3.

3?15?05?

10. To convert minutes and seconds into decimal parts of a degree,

divide the number of minutes by 60 and the number of seconds

by 3,600. Then add the numbers together. Write the location of

Roanoke, VA, as a decimal to the nearest thousandths of a degree.

125?

44?

?

acute

Holt Geometry

Copyright ? by Holt, Rinehart and Winston.

All rights reserved.

63

22

Holt Geometry

Holt Geometry

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