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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 . % ' & $ # 2. Name eight different angles in the figure. ⬔A, ⬔C, ⬔ABC, ⬔ABD, ⬔ADB, " ⬔ADC, ⬔CBD, and ⬔CDB $ ! 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 ��� �� � �� �� ��� �� ��� �� �� ��� ��� �� ��� � �� �� �� �� �� �� �� ��� ��� �� ��� � �� � 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