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Practice AFor use with the lesson “Describe Angle Pair Relationships”

Tell whether the indicated angles are adjacent.

1. ∠ BAC and ∠ CAD 2. ∠ EFG and ∠ HGF 3. ∠ JNM and ∠ LNK

D

C

B

A

H

E

F G

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L

K

M

N

Name a pair of complementary angles and a pair of supplementary angles.

4.

P SO358558

R 5.

208 1108 708

UXV

T W Y Z

∠ 1 and ∠ 2 are complementary angles. Given the measure of ∠ 1, find m∠ 2.

6. m∠ 1 5 528 7. m∠ 1 5 768 8. m∠ 1 5 198 9. m∠ 1 5 638

∠ 1 and ∠ 2 are supplementary angles. Given the measure of ∠ 1, find m∠ 2.

10. m∠ 1 5 1478 11. m∠ 1 5 948 12. m∠ 1 5 388 13. m∠ 1 5 1218

Find m∠ ABD and m∠ DBC.

14.

2x83x8

B EA

DC

15.

B CA

D

(11x 2 6)8(4x 1 6)8

16.

B

D

CA

(9x 2 11)8(10x 1 1)8

Use the diagram below. Tell whether the angles are vertical angles, a linear pair, or neither.

17. ∠ 1 and ∠ 2

5 6 7 8

34 2

1 18. ∠ 1 and ∠ 3

19. ∠ 2 and ∠ 4

20. ∠ 3 and ∠ 4

21. ∠ 5 and ∠ 6

22. ∠ 5 and ∠ 7

23. ∠ 6 and ∠ 8

24. ∠ 7 and ∠ 8

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Find the values of x and y.

25.

(9x 1 5)816x8

4y 8

26.

(6x 2 11)8 (20y 1 19)8

(2x 2 9)8

27.

(10x 1 7)8(9x 1 2)8

(18y 1 25)8

∠ A and ∠ B are complementary. Find m∠ A and m∠ B.

28. m∠ A 5 x8 29. m∠ A 5 (5x 1 4)8

m∠ B 5 (x 2 30)8 m∠ B 5 (7x 2 10)8

30. m∠ A 5 (4x 2 2)8 31. m∠ A 5 (6x 2 9)8

m∠ B 5 (11x 1 17)8 m∠ B 5 (8x 1 1)8

∠ A and ∠ B are supplementary. Find m∠ A and m∠ B.

32. m∠ A 5 x8 33. m∠ A 5 (7x 2 3)8

m∠ B 5 3x8 m∠ B 5 (x 2 1)8

34. m∠ A 5 (11x 1 2)8 35. m∠ A 5 (13x 1 10)8

m∠ B 5 (8x 1 7)8 m∠ B 5 (12x 1 20)8

36. Baseball The foul lines of a baseball field

Path of ball

648

intersect at home plate to form a right angle. You hit a baseball whose path forms an angle of 648 with the third base foul line (see figure at right). What is the angle between the first base foul line and the path of the baseball?

Stair Railing A stair railing is designed as 1

8 67

54

2 3

shown in the figure. Use the angles identified in the figure to name two pairs of the indicated type of angle pair.

37. Complementary angles

38. Supplementary angles

39. Vertical angles

40. Linear pair

41. Adjacent angles

Practice A continuedFor use with the lesson “Describe Angle Pair Relationships”

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Lesson Measure and Classify Angles, continued

Practice Level C

1. 548; acute 2. 908; right 3. 1098; obtuse

4. 1808; straight 5. ∠ MGH, ∠ HGL, and ∠ LGH; acute 6. ∠ GLK, ∠ KLM, ∠ MLK, and ∠ L; acute 7. ∠ MJK; obtuse 8. ∠ LKJ, ∠ GKL, ∠ LKG, and ∠ K; right 9. ∠ LMH, ∠ JML, and ∠ LMJ; obtuse 10. ∠ KJG; straight 11. 1478

12. 768 13. 56.58 14. 818 15. 33.58

16. m∠ JKM 5 518, m∠ JKL 5 1028

17. m∠ LKM 5 638, m∠ JKL 5 1268

18. m∠ JKM 5 39.58, m∠ LKM 5 39.58

19. 1068 20. 748 21. 678 22. 1578 23. 1188

24. 1628 25. 658

26.

x

y

1

1

A

BC

27.

x

y

1

2

AB

C

right; obtuse; Sample answer: (3, 3) Sample answer: (0, 1)

28. a. acute: ∠ AKB, ∠ CLD, ∠ DLE, ∠ FMG, ∠ BJH, ∠ EKF, ∠ ALH, ∠ GLH, ∠ BMC, and ∠ DJF; obtuse: ∠ BKE, ∠ ALD, ∠ DLG, ∠ CMF, ∠ BMG, ∠ FJH, ∠ BJD, ∠ CLH, ∠ HLE, and ∠ AKJ; right: ∠ ALC, ∠ CLE, ∠ ELG, and ∠ ALG b. ∠ DLE and ∠ ALH; ∠ CLD and ∠ GLH; ∠ AKB and ∠ EKF; ∠ BKE and ∠ AKF; ∠ BJH and ∠ DJF; ∠ BJD and ∠ FJH; ∠ BMC and ∠ FMG; ∠ BMG and ∠ CMF; ∠ DLA and ∠ HLE ∠ ALC, ∠ CLE, ∠ ELG, and ∠ ALG c. m∠ CLD 5 528, m∠ EKF 5 278, m∠ FJH 5 1158, m∠ FMG 5 638, m∠ DJF 5 658, m∠ DLG 5 1288

Study Guide

1. ∠JRM, ∠MRJ, ∠R; R, ###$ RJ , ###$ RM

2. ∠XYZ, ∠ZYX, ∠Y; Y, ###$ YX , ###$ YZ

3. ∠NML, ∠LMN, ∠M; M, ###$ ML , ####$ MN 4. 1258; ∠JRN is acute; ∠NRM is right; ∠JRM is obtuse.

5. 1208; ∠ABD is acute; ∠DBC is obtuse; ∠ABC is straight.

Problem Solving Workshop: Worked Out Example

1. 308 2. m∠DAB 5 788; m∠BCD 5 488; m∠ADB 5 518

Challenge Practice

1. Always; Sample answer: opposite rays form a straight line which is also a straight angle.

2. Sometimes; Sample answer: the sum of the two acute angles A and B where m∠ A 5 158 and m∠ B 5 108, is 258, which is not equal to 908.

3. Sometimes; Sample answer: it is not said whether or not ###$ DC bisects ∠ ADB.

4. Never; Sample answer: when a ray bisects an angle, it divides the angle into two congruent angles. Because the measure of a straight angle is 1808, the two congruent angles measure 908, which are right angles.

5.

A

B

CD

E F

958

1258

6. 47.58 7. 47.58 8. 172.58 9. 92.58

10. 1408 11. 1408

12. a. ∠ HOA > ∠ AOB > ∠ BOC > ∠ COD > ∠ DOE > ∠ EOF > ∠ FOG > ∠ GOH b. ∠ AOC, ∠ BOD, ∠ COE, ∠ DOF, ∠ EOG, ∠ FOH, ∠ GOA, ∠ HOB c. ∠ GOB > ∠ DOG > ∠ COH > ∠ COF > ∠ AOD > ∠ EOB > ∠ HOE > ∠ FOA d. Sample answer: ∠GOB and ∠COB

Lesson Describe Angle Pair RelationshipsTeaching Guide

1–3. Answers will vary. Students are discovering that vertical angles are congruent and that the sum of the measures of adjacent angles formed by intersecting lines is 1808.

Practice Level A

1. yes 2. no 3. no 4. complementary: ∠ POQ and ∠ ROS; supplementary: either ∠ POR and ∠ ROS or ∠ POQ and ∠ QOS

5. complementary: ∠ UTV and ∠ XYZ; supplementary: ∠ VTW and ∠ XYZ

6. 388 7. 148 8. 718 9. 278 10. 338 11. 868

12. 1428 13. 598

14. m∠ ABD 5 368, m∠ DBC 5 548

15. m∠ ABD 5 548, m∠ DBC 5 1268

16. m∠ ABD 5 1018, m∠ DBC 5 798

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Lesson Describe Angle Pair Relationships, continued17. linear pair 18. vertical angles

19. vertical angles 20. linear pair

21. linear pair 22. neither 23. neither

24. linear pair 25. x 5 7, y 5 17

26. x 5 25, y 5 6 27. x 5 9, y 5 4

28. m∠ A 5 608, m∠ B 5 308

29. m∠ A 5 448, m∠ B 5 468

30. m∠ A 5 188, m∠ B 5 728

31. m∠ A 5 338, m∠ B 5 578

32. m∠ A 5 458, m∠ B 5 1358

33. m∠ A 5 1588, m∠ B 5 228

34. m∠ A 5 1018, m∠ B 5 798

35. m∠ A 5 888, m∠ B 5 928 36. 268

37. ∠ 1 and ∠ 2, ∠ 3 and ∠ 4

38. Sample answer: ∠ 5 and ∠ 6, ∠ 7 and ∠ 8

39. ∠ 5 and ∠ 7, ∠ 6 and ∠ 8

40. Sample answer: ∠ 5 and ∠ 8, ∠ 6 and ∠ 7

41. Sample answer: ∠ 1 and ∠ 2, ∠ 5 and ∠ 6

Practice Level B

1. 108; 1708 2. 578; 1238 3. 188; 1628 4. 838; 978 5. 408; 508 6. 388; 1428 7. 858; 958

8. neither 9. neither 10. linear pair

11. vertical angles 12. vertical angles

13. 22.58; 67.58 14. 208; 1608 15. 718; 1098

16. x 5 10, y 5 8.25 17. x 5 5, y 5 50

18. x 5 13, y 5 23 19. x 5 6, y 5 24

20. x 5 3.25, y 5 5.5 21. x 5 21, y 5 35

22. never 23. always 24. sometimes

25. 558; 358 26. 508; 408 27. 32.48; 57.68

28. 608; 308 29. 658; 1158 30. 1508; 308

31. 1638; 178 32. 1608; 208

33. Sample answer: ∠ AIB and ∠ AIH, ∠ AJB and ∠ AJG 34. Sample answer: ∠ HBG and ∠GBC, ∠ BCF and ∠ FCE 35. Sample answer: ∠ AIB and ∠ HIJ, ∠ BIJ and ∠ AIH 36. Sample answer: ∠ AIB and ∠ AIH, ∠ AJB and ∠ AJG

37. Sample answer: ∠ AIB and ∠ AIH, ∠ AJB and ∠ AJG 38. The angle of elevation is increasing. The closer the plane gets, the higher up you have to look.

Practice Level C

1. m∠ 2 5 478, m∠ 3 5 1338 2. m∠ 2 5 628, m∠ 3 5 1188 3. m∠ 2 5 20.58, m∠ 3 5 159.58

4. m∠ 2 5 72.58, m∠ 3 5 107.58

5. m∠ ABC 5 648, m∠ CBD 5 268

6. m∠ ABC 5 978, m∠ CBD 5 838

7. m∠ ABC 5 112.58, m∠ CBD 5 67.58

8. linear pair 9. vertical angles

10. neither 11. neither 12. vertical angles

13. linear pair 14. neither 15. linear pair

16. 11.258 and 78.758 17. 11.258 and 168.758

18. 66.58 and 113.58 19. x 5 5, y 5 6

20. x 5 6, y 5 11 21. x 5 7.5, y 5 8.5

22. x 5 9.5, y 5 3.5 23. x 5 4, y 5 17

24. x 5 13.5, y 5 3.5 25. Never; Vertical angles do not share a common side. 26. Sometimes; This is true except when both angles are right angles. 27. Always; An angle that has a complement must have a measure less than 908, so there will always be another angle that would make the sum of the two angle measures equal 1808. 28. m∠ A 5 208, m∠ B 5 708

29. m∠ A 5 838, m∠ B 5 78 30. m∠ A 5 618, m∠ B 5 298 31. m∠ A 5 43.58, m∠ B 5 46.58

32. m∠ A 5 1038, m∠ B 5 778 33. m∠ A 5  248, m∠ B 5 1568 34. m∠ A 5 67.58, m∠ B 5 112.58

35. m∠ A 5 1418, m∠ B 5 398

36. supplementary 37. supplementary

38. complementary

39. Sample answer: ∠ 3 and ∠ 4, ∠ 7 and ∠ 10

40. Sample answer: ∠ 2 and ∠ 4, ∠ 3 and ∠ 541. Sample answer: ∠ 2 and ∠ 3, ∠ 4 and ∠ 542. Sample answer: ∠ 7 an d ∠ 8, ∠ 9 and ∠ 10

43. 10; 20; 20

Study Guide

1. ∠DBC and ∠MNO, ∠ABD and ∠MNO, ∠ABD and ∠DBC 2. 358 3. 1008 4. linear pairs: ∠3 and ∠4, ∠4 and ∠5; vertical angles: ∠3 and ∠5 5. 908, 908, 908 6. 308, 1208, 608

7. 458, 1358, 458

Interdisciplinary Application

1. m∠BDC 5 508 2. m∠FDE 5 508

3. m∠FDK 5 358 4. The keys are closer to you than you thought.

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