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Name LESSON 1-4 Date Class Practice B Pairs of Angles 180 1. ⬔PQR and ⬔SQR form a linear pair. Find the sum of their measures. ___› QR 2. Name the ray that ⬔PQR and ⬔SQR share. Use the figures for Exercises 3 and 4. 137.9 3. supplement of ⬔Z 4. complement of ⬔Y X : (110 8x) 9 5. An angle measures 12 degrees less than three times its supplement. Find the measure of the angle. 132 6. An angle is its own complement. Find the measure of a supplement to this angle. 135 7. ⬔DEF and ⬔FEG are complementary. m⬔DEF (3x 4)°, and m⬔FEG (5x 6)°. Find the measures of both angles. m⬔DEF 29; m⬔FEG 61 8. ⬔DEF and ⬔FEG are supplementary. m⬔DEF (9x 1)°, and m⬔FEG (8x 9)°. Find the measures of both angles. m⬔DEF 91; m⬔FEG 89 Use the figure for Exercises 9 and 10. In 2004, several nickels were minted to commemorate the Louisiana Purchase and Lewis and Clark’s expedition into the American West. One nickel shows a pipe and a hatchet crossed to symbolize peace between the American government and Native American tribes. 9. Name a pair of vertical angles. Possible answers: ⬔1 and ⬔3 or ⬔2 and ⬔4 10. Name a linear pair of angles. Possible answers: ⬔1 and ⬔2; ⬔2 and ⬔3; ⬔3 and ⬔4; or ⬔1 and ⬔4 11. ⬔ABC and ⬔CBD form a linear pair and have equal measures. Tell if ⬔ABC is acute, right, or obtuse. right __› 12. ⬔KLM and ⬔MLN are complementary. LM bisects ⬔KLN. Find the measures of ⬔KLM and ⬔MLN. Copyright © by Holt, Rinehart and Winston. All rights reserved. 28 45°; 45° Holt Geometry Name LESSON 1-4 Date Class Name Practice A 1-4 Complete the statements. side , but no common interior points. Use the figures for Exercises 3 and 4. 90� 4. complement of �Y . 5. measure of the angle. . angles are two angles whose measures Find the measures of both angles. m�DEF �������������� Find the measures of both angles. m�DEF 9. Name a pair of vertical angles. � � Possible answers: �1 and �3 In an equilateral triangle, all three sides have equal lengths and all three angles have equal measures. Find the measure of the following angles. 9. supplement of �A 120� 30� or �2 and �4 11. �ABC and �CBD form a linear pair and have equal measures. Tell if �ABC is acute, right, or obtuse. �������������� 27 Copyright © by Holt, Rinehart and Winston. All rights reserved. Name right __› 12. �KLM and �MLN are complementary. LM bisects �KLN. Find the measures of �KLM and �MLN. � � 1-4 � � Possible answers: �1 and �2; �2 and �3; �3 and �4; or �1 and �4 ��� Draw your answer in the space provided. LESSON � � 10. Name a linear pair of angles. � 11. Sketch �1 and �2 so that they are vertical angles. � 91�; m�FEG � 89� Use the figure for Exercises 9 and 10. In 2004, several nickels were minted to commemorate the Louisiana Purchase and Lewis and Clark’s expedition into the American West. One nickel shows a pipe and a hatchet crossed to symbolize peace between the American government and Native American tribes. � �������������� 10. complement of �A � 29�; m�FEG � 61� 8. �DEF and �FEG are supplementary. m�DEF � (9x � 1)°, and m�FEG � (8x � 9)°. � 8. Sketch �1 and �2 so that they form a linear pair. 132� 7. �DEF and �FEG are complementary. m�DEF � (3x � 4)°, and m�FEG � (5x � 6)°. . Draw your answer in the space provided. 7. Sketch �1 and �2 so that they are adjacent angles. ����� 135� 6. The kind of angle formed by the noncommon sides of two adjacent and straight angle � 6. An angle is its own complement. Find the measure of a supplement to this angle. have a sum of 180�. supplementary angles is a (110 � 8x)� 5. An angle measures 12 degrees less than three times its supplement. Find the 4. The kind of angle formed by the noncommon sides of two adjacent and Supplementary Date Holt Geometry Class Name LESSON 1-4 Pairs of Angles Draw your answers in the space provided. 1. Draw two intersecting lines and label the resulting angles with the numbers 1, 2, 3, and 4. 2. Label �1 with x �. �1 and �2 are supplementary. Find the measure of �2 and label the diagram. 45°; 45° 28 Copyright © by Holt, Rinehart and Winston. All rights reserved. Practice C Date Pairs of Angles Angle Pairs �������������� �������� �� � �� � � �� � Adjacent Angles have the same vertex and share a common side Linear Pairs adjacent angles whose noncommon sides are opposite rays Vertical Angles nonadjacent angles formed by two intersecting lines 3. �3 is also supplementary to �2. Find the measure of �3 and label the diagram. � � � � The measures of the vertical angles are equal. �1 and �2 are adjacent. 5. �X is complementary to �Y, and �Z is also complementary to �Y. Explain why �X and �Z are congruent. � � �3 and �4 are adjacent and form a linear pair. �5 and �6 are vertical angles. Tell whether �7 and �8 in each figure are only adjacent, are adjacent and form a linear pair, or are not adjacent. If m�X � m�Y � 90� and m�Z � m�Y � 90�, then m�X and m�Z 2. 1. are both equal to 90� � m�Y. So m�X � m�Z. Two angles whose � � measures are equal are congruent. Adjacent angles are defined as two angles in the same plane with a common vertex and a common side, but no common interior points. 3. � adjacent and form a linear pair 6. �ADB and �CDB are adjacent angles. If the phrase “but no common interior points” was not part of the definition, name another pair of angles that would qualify as adjacent. � � only adjacent not adjacent only adjacent 4. �5 and �4 � � Draw your answer in the space provided. 7. Draw a diagram that shows why the definition of adjacent angles includes the phrase “in the same plane.” Use the figure for Exercises 8 –10. 9. �3 is a right angle 60� Copyright © by Holt, Rinehart and Winston. All rights reserved. 45� 29 Copyright © by Holt, Rinehart and Winston. All rights reserved. 5. �1 and �4 not adjacent 6. �2 and �3 adjacent and form a linear pair Name each of the following. 7. a pair of vertical angles � � � Tell whether the indicated angles are only adjacent, are adjacent and form a linear pair, or are not adjacent. Possible answer: �ADB and �ADC This diagram shows a ray of light reflecting off a mirror. When light reflects, the incident angle and the reflected angle are congruent, that is, �1 � �2. Find the measure of �1 in each situation below. Holt Geometry Class Reteach 4. From your work in Exercises 1–3, make a conclusion about the measures of the vertical angles. 8. �1 � �3 � ���������� 137.9� 3. supplement of �Z 3. Complementary angles are two angles whose measures have a sum of right angle 180� ___› QR 2. Name the ray that �PQR and �SQR share. 2. A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays. complementary angles is a Pairs of Angles 1. �PQR and �SQR form a linear pair. Find the sum of their measures. vertex 1. Adjacent angles are two angles in the same plane with a common Class Practice B LESSON Pairs of Angles and a common Date � 10. m�1 � 2m�3 8. a linear pair � Possible answers: �1 and �6, �2 and �5 Possible answers: �1 and �2; �1 and �5; �5 and �6; �6 and �2 � 72� 9. an angle adjacent to �4 Holt Geometry Copyright © by Holt, Rinehart and Winston. All rights reserved. 65 � � � � � � � �3 30 Holt Geometry Holt Geometry