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NameDateDescribing Pairs of Angles1.6For use with Exploration 1.6Essential Question How can you describe angle pair relationships anduse these descriptions to find angle measures?1EXPLORATION: Finding Angle MeasuresWork with a partner. The five-pointed star has a regular pentagon at its center.a. What do you notice about the following angle pairs?x and y v y z w x 108 y and z x and z b. Find the values of the indicated variables. Do not use a protractor to measurethe angles.x y z w v Explain how you obtained each answer.Copyright Big Ideas Learning, LLCAll rights reserved.GeometryStudent Journal27

Name Date1.62Describing Pairs of Angles (continued)EXPLORATION: Finding Angle MeasuresWork with a partner. A square is divided by its diagonals into four triangles.a. What do you notice about the following angle pairs?a and b c and d e d c c and e b b. Find the values of the indicated variables. Do not use aa protractor to measure the angles.c d e Explain how you obtained each answer.Communicate Your Answer3. How can you describe angle pair relationships and use these descriptions to findangle measures?4. What do you notice about the angle measures of complementary angles,supplementary angles, and vertical angles?28GeometryStudent JournalCopyright Big Ideas Learning, LLCAll rights reserved.

Name1.6DateNotetaking with VocabularyFor use after Lesson 1.6In your own words, write the meaning of each vocabulary term.complementary anglessupplementary anglesadjacent angleslinear pairvertical anglesCore ConceptsComplementary and Supplementary AnglesCA115 20 170 2B 1 and 2 A and Bcomplementary anglesTwo positive angles whose measures havea sum of 90 . Each angle is the complementof the other.65 3 4 3 and 4D C and Dsupplementary anglesTwo positive angles whose measures have asum of 180 . Each angle is the supplementof the other.Notes:Copyright Big Ideas Learning, LLCAll rights reserved.GeometryStudent Journal29

Name Date1.6Notetaking with Vocabulary (continued)Adjacent AnglesComplementary angles and supplementary angles can be adjacent angles or nonadjacentangles. Adjacent angles are two angles that share a common vertex and side, but haveno common interior points.common side5768common vertex 5 and 6 are adjacent angles 7 and 8 are nonadjacent angles.Notes:Linear Pairs and Vertical AnglesTwo adjacent angles are a linear pair whentheir noncommon sides are opposite rays. Theangles in a linear pair are supplementary angles.Two angles are vertical angles whentheir sides form two pairs of oppositerays.common side31 2noncommon side noncommon side 1 and 2 are a linear pair.456 3 and 6 are vertical angles. 4 and 5 are vertical angles.Notes:30GeometryStudent JournalCopyright Big Ideas Learning, LLCAll rights reserved.

Name DateNotetaking with Vocabulary (continued)1.6Extra PracticeIn Exercises 1 and 2, use the figure.P1. Name the pair(s) of adjacent complementary angles.LKT15 15 2. Name the pair(s) of nonadjacent supplementary angles.Jm A 36 . Find m B.QR105 MIn Exercises 3 and 4, find the angle measure.3. A is a complement of B andS105 75 O75 4. C is a supplement of D andm D 117 . Find m C.In Exercises 5 and 6, find the measure of each angle.5.6.AB(10x 22) CE(6x 5) HF (12x 5) (7x 34) DGIn Exercises 7 –9, use the figure.7. Identify the linear pair(s) that include 1.148. Identify the vertical angles.9. Are 6 and 7 a linear pair? Explain.Copyright Big Ideas Learning, LLCAll rights reserved.235106978GeometryStudent Journal31

Adjacent angles are two angles that share a common vertex and side, but have no common interior points. 5 and 6 are adjacent angles 7 and 8 are nonadjacent angles. Notes: Linear Pairs and Vertical Angles Two adjacent angles are a linear pair when Two angles are vertical angles when their noncommon sides are opposite rays.

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