Download 1-3 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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!
9
8
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° and m⬔RQT 11.
14
7. m⬔PQR if m⬔PQR (10x 7), m⬔RQT 5x °, 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°4225. Roanoke, VA, is located at 79°5730. 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– 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
��� ��
�
�� �� ���
�� ���
��
��
���
���
��
���
� �� ��
��
��
��
��
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�� ���
�
��
�
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° 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 °, 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°42�25�. Roanoke, VA, is located at 79°57�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°). 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°
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° 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°). 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 1–3.
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