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NAME1-5DATEPERIODSkills PracticeAngle RelationshipsFor Exercises 1–6, use the figure at the right. Name anangle or angle pair that satisfies each condition.EF1. Name two acute vertical angles.K2. Name two obtuse vertical angles.HGJ3. Name a linear pair.4. Name two acute adjacent angles.5. Name an angle complementary to EKH.6. Name an angle supplementary to FKG.7. Find the measures of an angle and its complement if one angle measures 24 degreesmore than the other.8. The measure of the supplement of an angle is 36 less than the measure of the angle.Find the measures of the angles.R . TS9. If m RTS 8x 18, find the value of x so that TR10. If m PTQ 3y - 10 and m QTR y, find the value of yso that PTR is a right angle.QPTDetermine whether each statement can be assumedfrom the figure. Explain.SWV11. WZU is a right angle.XZUY12. YZU and UZV are supplementary.13. VZU is adjacent to YZX.Lesson 1-5Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ALGEBRA For Exercises 9–10, use the figure at the right.Chapter 133Glencoe Geometry

NAME1-5DATEPERIODPracticeAngle RelationshipsName an angle or angle pair that satisfies each condition.GH50 F1. Name two obtuse vertical angles.CB2. Name a linear pair whose vertex is B.50 3. Name an angle not adjacent to, but complementaryto FGC.AED4. Name an angle adjacent and supplementary to DCB.5. ALGEBRA Two angles are complementary. The measure of one angle is 21 more thantwice the measure of the other angle. Find the measures of the angles.6. ALGEBRA If a supplement of an angle has a measure 78 less than the measure of theangle, what are the measures of the angles?ALGEBRA For Exercises 7–8, use the figure atAthe right.B7. If m FGE 5x 10, find the value of x so that AE .FCCGFEDetermine whether each statement can beassumed from the figure. Explain.NO9. NQO and OQP are complementary.PQM10. SRQ and QRP is a linear pair.RChapter 134aco12. STREET MAPS Darren sketched a map of the cross streetsnearest to his home for his friend Miguel. Describe twodifferent angle relationships between the streets.Be11. MQN and MQR are vertical angles.nSOliveMainGlencoe GeometryCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.D8. If m BGC 16x - 4 and m CGD 2x 13,find the value of x so that BGD is a right angle.

NAME1-5DATEPERIODStudy Guide and InterventionAngle RelationshipsPairs of Angles Adjacent angles are two angles that lie in the same plane and have acommon vertex and a common side, but no common interior points. A pair of adjacent angleswith noncommon sides that are opposite rays is called a linear pair. Vertical angles aretwo nonadjacent angles formed by two intersecting lines.ExampleName an angle or angle pair that satisfies each condition.a. two vertical angles EFI and GFH are nonadjacent anglesformed by two intersecting lines. They arevertical angles.%(&"'#b. two adjacent angles)* ABD and DBE have a common vertex anda common side but no common interior points.They are adjacent angles.c. two supplementary angles EFG and GFH form a linear pair. The angles are supplementary.d. two complementary anglesExercisesName an angle or angle pair that satisfies each condition.1. two adjacent anglesL2. two acute vertical angles3. two supplementary adjacent anglesN110 RTE4. an angle supplementary to RTSSFor Exercises 5–7, use the figure at the right.5. Identify two obtuse vertical angles.SRV6. Identify two acute adjacent angles.NU7. Identify an angle supplementary to TNU.T8. Find the measures of two complementary angles if the difference in their measures is 18.Chapter 131Glencoe GeometryLesson 1-5Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.m CBD m DBE 90. These angles are complementary.

NAME1-5DATEStudy Guide and InterventionPERIOD(continued)Angle RelationshipsPerpendicular LinesLines, rays, and segments that form fourright angles are perpendicular. The right angle symbol indicates that is perpendicularthe lines are perpendicular. In the figure at the right, AC BD , or AC .to BDExampleABCD and ZP are perpendicular.Find x so that DZ ZP , then m DZP 90.If DZm DZQ m QZP m DZP(9x 5) (3x 1) 9012x 6 9012x 84x 7DQ(9x 5) (3x 1) Sum of parts wholeSubstitutionZPCombine like terms.Subtract 6 from each side.Divide each side by 12.Exercises . MQ1. Find the value of x and y so that NRNP2. Find m MSN.5x Mx (9y 18) SQ BF . Find3. m EBF 3x 10, m DBE x, and BDthe value of x.ED4. If m EBF 7y - 3 and m FBC 3y 3, find the value of y . BCso that EBFBAC5. Find the value of x, m PQS, and m SQR.PS3x (8x 2) QR6. Find the value of y, m RPT, and m TPW.T(4y - 5) (2y 5) RPWVSChapter 132Glencoe GeometryCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.R

NAME1-5DATEPERIODWord Problem PracticeAngle Relationships1. LETTERS A sign painter is painting alarge “X”. What are the measures ofangles 1, 2, and 3?4. GLASS Carlo dropped a piece of stainedglass and the glass shattered. He pickedup the piece shown on the left.21120 3?106 Part of edge2He wanted to find the piece that wasadjoining on the right. What should themeasurement of the angle marked witha question mark be? How is that anglerelated to the angle marked 106 ?5. LAYOUTS A rectangular plaza has awalking path along its perimeter inaddition to two paths that cut across theplaza as shown in the figure.Cut13. PIZZA Ralph has sliced a pizza usingstraight line cuts through the center ofthe pizza. The slices are not exactly thesame size. Ralph notices that twoadjacent slices are complementary. Ifone of the slices has a measure of 2xº,and the other a measure of 3xº, what isthe measure of each angle?1135 32450 a. Find the measure of 1.b. Find the measure of 4.c. Name a pair of vertical angles in thefigure. What is the measure of 2?Chapter 135Glencoe GeometryLesson 1-5Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2. PAPER Matthew cuts a straight linesegment through a rectangular sheet ofpaper. His cuts goes right through acorner. How are the two angles formedat that corner related?Missing Piece

Name an angle or angle pair that satisfies each condition. 1. Name two obtuse vertical angles. 2. Name a linear pair whose vertex is B. 3. Name an angle not adjacent to, but complementary to FGC. 4. Name an angle adjacent and supplementary to DCB. 5. ALGEBRA Two angles are complementary. The measure of one angle is 21 more than

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