chapter 7 test, review

Name: ________________________ Class: ___________________ Date: __________ ID: A

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Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. The measure of ∠A is 180°. What type of angle is ∠A?

a. acute b. obtuse c. straight d. right

____ 2. Find the complement of an angle that measures 73°.

a. 253° b. 17° c. 107° d. 163°

____ 3. Find the supplement of an angle that measures 53°.

a. 143° b. 127° c. 233° d. 37°

____ 4. Find the measure of ∠BOC.

a. 144° b. 149° c. 59° d. 64°

____ 5. Find the measure of ∠ABC.

a. 234° b. 36° c. 126° d. 144°

____ 6. Find the supplement of ∠AOC.

a. 136° b. 134° c. 226° d. 44°

Name: ________________________ ID: A

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____ 7. Name the angle that is supplementary to ∠AOF.

a. ∠BOC b. ∠FOB c. ∠AOD d. ∠FOD

____ 8. Name a pair of opposite angles.

a. ∠BOC and ∠COD c. ∠AOB and ∠COD

b. ∠AOB and ∠DOB d. ∠AOF and ∠COD

____ 9. Find the measure of ∠AED if ∠BEC = ∠34°.

a. 68° b. 34° c. 146° d. 292°

____ 10. Marci measured ∠AOD in the intersection of 2 walkways. ∠AOD = 98°.

What is the measure of ∠COB?

a. 188° b. 98° c. 82° d. 196°

Name: ________________________ ID: A

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____ 11. What is the measure of ∠AOC?

a. 71° b. 109° c. 289° d. 199°

____ 12. Find the measure of ∠AEB if measure of ∠BEC = ∠117°.

a. 117° b. 63° c. 234° d. 126°

____ 13. Name 2 angles that are complementary to ∠AOC.

a. ∠COD and ∠AOE c. ∠COD and ∠DOE

b. ∠DOE and ∠BOC d. ∠AOB and ∠BOC

____ 14. The measure of ∠2 is 110°. Find the measure of ∠1.

a. 65° b. 115° c. 110° d. 70°

____ 15. The measures of the 3 angles in a triangle are 113°, 47°, and 20°. Classify the triangle.

a. acute b. right c. straight d. obtuse

Name: ________________________ ID: A

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____ 16. Find the measure of ∠A in this triangle.

a. 112° b. 22° c. 158° d. 68°

____ 17. Find the measure of ∠A in this triangle.

a. 128° b. 218° c. 52° d. 142°

____ 18. Find the measure of ∠Q in this triangle.

a. 69° b. 111° c. 115° d. 19°

Name: ________________________ ID: A

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____ 19. Find the measure of ∠B in this triangle.

a. 287° b. 1° c. 107° d. 73°

____ 20. The measures of 2 angles of a triangle are 140° and 13°.

Find the measure of the third angle.

a. 127° b. 27° c. 153° d. 63°

____ 21. The measures of 2 angles in a triangle are 53° and 77°.

Find the measure of the third angle and classify the triangle according to its angles.

a. 193°, right b. 193°, acute c. 50°, right d. 50°, acute

____ 22. Find the measure of ∠ABC in this diagram.

a. 48° b. 132° c. 62° d. 160°

____ 23. Find the measures of ∠ACB, ∠BCD, and ∠BDC in this diagram.

a. 94°, 72°, 86° b. 94°, 86°, 72° c. 86°, 72°, 94° d. 86°, 94°, 72°

____ 24. A triangle has an angle of 102°, which is twice the measure of another angle in the triangle.

What are the measures of the 3 angles?

a. 27°, 51°, 102° b. 37°, 51°, 102° c. 37°, 51°, 107° d. 51°, 102°, 153°

Name: ________________________ ID: A

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____ 25. Which angle is an interior angle?

a. ∠BFE b. ∠DGH c. ∠FGD d. ∠AFE

____ 26. A transversal intersects 2 parallel lines. Which statement is true?

a. The alternate angles are equal.

b. The interior angles are complementary.

c. The corresponding angles are supplementary.

d. None of these

____ 27. A transversal intersects 2 parallel lines. Complete this statement:

The ____ angles are supplementary.

a. acute b. interior c. corresponding d. alternate

____ 28. How many pairs of corresponding angles are formed by a transversal intersecting two lines?

a. 8 b. 6 c. 2 d. 4

____ 29. In this diagram, ∠4 = 42°, what is the measure of ∠5?

a. 34° b. 42° c. 47° d. 44°

____ 30. In this diagram, find the measure of ∠5.

a. 134° b. 226° c. 234° d. 216°

Name: ________________________ ID: A

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____ 31. In this diagram, find the measure of ∠CGH.

a. 140° b. 35° c. 40° d. 130°

____ 32. In this diagram, identify the pair of angles e and b as “Corresponding,” “Alternate,” “Both,” or “Neither.”

a. Alternate b. Neither c. Both d. Corresponding

____ 33. Are the 2 line segments AB and CD parallel? Explain.

a. Yes; corresponding angles are equal.

b. No; corresponding angles are not equal.

c. Yes; alternate angles are equal.

d. No; alternate angles are not equal.

Name: ________________________ ID: A

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Parallel Lines

____ 34. In the Parallel Lines diagram, name the corresponding angle of ∠3.

a. ∠8 b. ∠2 c. ∠6 d. ∠7

____ 35. In the Parallel Lines diagram, name the alternate angle of ∠2.

a. ∠5 b. ∠3 c. ∠8 d. ∠7

____ 36. In the Parallel Lines diagram, ∠6 = 77°. What is the measure of ∠4?

a. 283° b. 103° c. 38.5° d. 77°

Parallel Airport Runways

____ 37. In the Airport Runways diagram, how are ∠1 and ∠5 related?

a. Corresponding angles c. Alternate angles

b. Interior angles d. None of these

____ 38. In the Airport Runways diagram, ∠8 measures 112°. What is the sum of the measures of ∠1 and ∠4?

a. 112° b. 224° c. 292° d. 136°

Name: ________________________ ID: A

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____ 39. In this diagram, find the value of x.

a. 70 b. 110 c. 80 d. 117

____ 40. In this diagram, find the value of y.

a. 54 b. 153 c. 81 d. 27

____ 41. Find the value of x in this diagram.

a. 32 b. 45 c. 22 d. 67

____ 42. Find the measure of ∠P in this diagram.

a. 45° b. 15° c. 19° d. 75°

Name: ________________________ ID: A

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____ 43. In this diagram, KQ is the bisector of ∠PQT. Find the measure of ∠KPQ.

a. 34° b. 45° c. 56° d. 68°

____ 44. In this diagram, ∆ABD is isosceles with ∠A = 66°. Find the measure of ∠ADC.

a. 114° b. 66° c. 42° d. 48°

____ 45. In this diagram ∆PQR is a right angled triangle. SV is parallel to QR and RV is perpendicular to SV.

Which angle is NOT complementary to ∠PRV?

a. ∠VTR b. ∠PTS c. ∠PST d. ∠PRQ

Name: ________________________ ID: A

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____ 46. In this diagram, ∆ACD is a right angled triangle. BF is parallel to CD and FC bisects ∠C.

Find the measure of ∠CFD.

a. 90° b. 116° c. 64° d. 38°

____ 47. In this diagram, ∆ABC is isosceles with AB = AC. CQ bisects ∠C and PQ is parallel to CB.

Find the measure of ∠BQC.

a. 29° b. 90° c. 58° d. 93°

____ 48. In this diagram, RQ is parallel to AB and PQ is parallel to AC. Find the measure of ∠A.

a. 38° b. 64° c. 26° d. 116°

Name: ________________________ ID: A

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____ 49. In this diagram, S is the meeting point of the bisectors of ∠P and ∠R.

Find the measure of ∠PSR.

a. 138° c. 42°

b. 84° d. cannot be determined

____ 50. Find the values of x, y and z in this diagram.

Find the values of x, y, and z.

a. x = 87°; y = 93°; z = 0° c. x = 93°; y = 39°; z = 87°

b. x = 93°; y = 87°; z = 53° d. x = 40°; y = 140°; z = 93°

Short Answer

51. Name this angle in 3 different ways.

Name: ________________________ ID: A

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52. a) Name 2 angles that are supplementary to ∠BOF.

b) Name 2 angles that are complementary to ∠BOF.

53. Find the measures of ∠BOC, ∠AOE, and ∠EOD.

54. Two angles are supplementary. One angle measures x° and the other measures y°.

a) Write a relationship between these 2 angles.

b) Find the value of y if x° = 62°.

55. Find the measure of ∠D in ∆DEF.

56. In ∆PQR, ∠P = 90° and ∠Q = 67°. Find the measure of ∠R.

Name: ________________________ ID: A

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57. Find the measure of ∠P in ∆PQR.

58. Find the measure of each angle in ∆ABC. Explain.

59. Figure ABCDEFGH is a regular octagon. Find the measure of each angle in the octagon.

60. In this diagram, ∆TUV and ∆WXV are congruent. Find these missing measures.

a) VX

b) WV

c) ∠T

d) ∠U

Name: ________________________ ID: A

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61. Find the measure of each angle labelled with a variable in this diagram.

62. One angle in a triangle is 100°. This is twice the measure of another angle in the same triangle.

Draw the triangle and label all its angle measures.

63. Find the values of the variables in this diagram.

64. In this diagram, ∠BFE = x + 10° and ∠DGH = 2x − 5°.

Find the measures of ∠BFE and ∠DGF.

Name: ________________________ ID: A

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Problem

65. a) Name pairs of opposite angles that are supplementary.

b) Name pairs of opposite angles that are complementary.

66. Is it possible to draw a pair of supplementary angles so that neither of the angles is obtuse? Explain.

67. In this diagram, ∠AGF = ∠BGC and ∠AGB = 130°.

Find the measure of these angles.

a) ∠BGC

b) ∠BGD

c) ∠DGE

Show your work.

68. Find the measure of ∠RVT. Explain your reasoning.

Name: ________________________ ID: A

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69. James is making a quilt using this pattern for each quilt square.

a) If ∠EDF = 31°, what is the measure of ∠CDE? Explain your answer.

b) If ∠BCD = ∠CDE, what do you know about the measure of ∠ACB? Explain your reasoning.

70. Find the measure of ∠CDE. Show your work.

71. Find the measure of ∠Q in ∆PQR. Show your work.

72. Figure ABCD is a kite with ∠B = 90°.

Find the measure of ∠BDC. Explain your answer.

Name: ________________________ ID: A

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73. Find the measure of ∠R in this circle. Explain your answer.

74. In figure ABCD, AB = AD, AC = BC = CD, and ∠BAD = 44°.

Find the measure of ∠BCD. Show your work.

75. In this diagram, SR is parallel to PQ and PQ = PR. Find the measure of ∠S.

Justify your answer.

Name: ________________________ ID: A

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76. In this diagram, PR is parallel to AC and BQ is parallel to DR.

Name an angle that is:

a) an alternate angle of ∠PQB and ∠BCD

b) a corresponding angle of ∠PQB and ∠BCD

c) an interior angle of ∠QBC and ∠R.

77. In this diagram, AB, CD, and EF are parallel line segments. BC and DE are parallel and DE = DF.

Find the measure of ∠B. Justify your answer.

78. In this diagram, AB is a diameter of the circle with centre at O. AC is parallel to OD.

Find the measure of ∠ACD. Show your work.

Name: ________________________ ID: A

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79. In this diagram, ABCD is a trapezoid. AB is parallel to DC and AB = AD. ∠DBC = 90°.

Find the measures of ∠BCD and ∠BDC. Justify your answers.

80. This diagram shows a circle with centre at O. A, B, and C are points on the circle.

Find the measure of ∠ABC. Explain your work.

81. In this diagram, ∆ABC is equilateral, AD = DE, and ∠BAD = 90°.

Find the value of x. Justify your answer.

Name: ________________________ ID: A

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82. In this diagram, QC is parallel to PS and BQ is parallel to SR.

Find the measure of ∠Q. Explain your work.

83. In this diagram, ∆ACD is right angled at A. BA is parallel to CD and AB = AC.

Find the measure of ∠D. Justify your answer.

84. In this diagram, PQLK is a parallelogram with KL extended to M.

Find the measures of ∠PLQ and ∠KPQ. Show your work.

ID: A

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Answer Section

MULTIPLE CHOICE

1. ANS: C PTS: 1 DIF: Easy

REF: 7.1 Angle Properties of Intersecting Lines STA: 8m48

TOP: Geometry and Spatial Sense KEY: Knowledge and Understanding

2. ANS: B PTS: 1 DIF: Easy






4. ANS: C PTS: 1 DIF: Moderate



5. ANS: B PTS: 1 DIF: Moderate






7. ANS: D PTS: 1 DIF: Moderate












11. ANS: A PTS: 1 DIF: Moderate












ID: A

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15. ANS: D PTS: 1 DIF: Easy REF: 7.2 Angles in a Triangle

STA: 8m48 TOP: Geometry and Spatial Sense KEY: Knowledge and Understanding

16. ANS: B PTS: 1 DIF: Easy REF: 7.2 Angles in a Triangle


17. ANS: C PTS: 1 DIF: Easy REF: 7.2 Angles in a Triangle


18. ANS: A PTS: 1 DIF: Easy REF: 7.2 Angles in a Triangle


19. ANS: D PTS: 1 DIF: Easy REF: 7.2 Angles in a Triangle


20. ANS: B PTS: 1 DIF: Moderate REF: 7.2 Angles in a Triangle


21. ANS: D PTS: 1 DIF: Moderate REF: 7.2 Angles in a Triangle


22. ANS: A PTS: 1 DIF: Moderate REF: 7.2 Angles in a Triangle


23. ANS: D PTS: 1 DIF: Moderate REF: 7.2 Angles in a Triangle


24. ANS: A PTS: 1 DIF: Moderate REF: 7.2 Angles in a Triangle

STA: 8m48 TOP: Geometry and Spatial Sense KEY: Thinking


REF: 7.3 Angle Properties of Parallel Lines STA: 8m48


26. ANS: A PTS: 1 DIF: Easy
























ID: A

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34. ANS: D PTS: 1 DIF: Easy



35. ANS: D PTS: 1 DIF: Easy



















REF: 7.6 Creating and Solving Geometry Problems STA: 8m48













TOP: Geometry and Spatial Sense KEY: Thinking













ID: A

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50. ANS: B PTS: 1 DIF: Difficult



SHORT ANSWER

51. ANS:

Answers may vary. Sample: ∠1, ∠M, ∠LMN

PTS: 1 DIF: Moderate REF: 7.1 Angle Properties of Intersecting Lines


52. ANS:

a) ∠BOE and ∠AOF

b) ∠BOD and ∠AOC



53. ANS:

∠BOC = 60°, ∠AOE = 30°, and ∠EOD = 150°



54. ANS:

a) Answers may vary. Sample:

x° + y° = 180°

b) y° = 118°



55. ANS:

∠D = 107°

PTS: 1 DIF: Easy REF: 7.2 Angles in a Triangle


56. ANS:

∠R = 23°

PTS: 1 DIF: Easy REF: 7.2 Angles in a Triangle


57. ANS:

∠P = 11°

PTS: 1 DIF: Moderate REF: 7.2 Angles in a Triangle


ID: A

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58. ANS:

∠A = 80°

∠B = 60°

∠C = 40°



59. ANS:

∠A = ∠B = ∠C = ∠D = ∠E = ∠F = ∠G = ∠H = 135°



60. ANS:

a) 3 m

b) 4.2 m

c) 45°

d) 100°

PTS: 1 DIF: Easy REF: 7.6 Creating and Solving Geometry Problems


61. ANS:

a = b = c = 90°

d = 122°, e = f = 58°

h = 32°, g = k = 148°

PTS: 1 DIF: Moderate REF: 7.6 Creating and Solving Geometry Problems


62. ANS:

Triangles may vary. Sample:


STA: 8m48 TOP: Geometry and Spatial Sense KEY: Communication

63. ANS:

w = y = 59°

x = v = 121°

z = 53°



ID: A

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64. ANS:

∠BFE = ∠DGF = 25°



PROBLEM

65. ANS:

a) ∠PWR and ∠VWS, ∠PWV and ∠RWS

b) ∠PWQ and ∠TWS, ∠QWR and ∠VWT

PTS: 1 DIF: Difficult REF: 7.1 Angle Properties of Intersecting Lines


66. ANS:

Explanations may vary. Sample:

Yes; draw 2 right angles (90°) next to each other.

The result is a pair of supplementary angles with no obtuse angles.



67. ANS:

a) ∠BGC =1

2180° − ∠AGB( )

=1

2180° − 130°( )

= 25°

b) ∠BGD = ∠BGC + ∠CGD

∠CGD = ∠AGF = ∠BGC

∠BGD = 2 × ∠BGC = 2 × 25° = 50°

c) ∠DGE = 90° − ∠CGD

= 90° − ∠BGC

= 90° − 25°

= 65°



ID: A

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68. ANS:


∠RVT = ∠RVS + ∠SVT

= 2 × ∠SVT

Since ∠PVT is a straight angle, ∠PVQ and ∠QVT are supplementary.

∠QVT = 180° − ∠PVQ

= 180° − ∠27°

= 153°

∠QVR = ∠RVS = ∠SVT =∠QVT

3

∠QVR =153°

3= 51°

∠RVT = 2 × ∠SVT

= 2 × 51°

= 102°



69. ANS:


a) Since ∠EDF and ∠CDE are supplementary,

∠EDF + ∠CDE = 180°

Substitute ∠EDF = 31°.

31° + ∠CDE = 180°

∠CDE = 180° − 31°

= 149°

The measure of ∠CDE is 149°.

b) Since ∠ACB and ∠BCD are supplementary,

∠ACB = 180° − ∠BCD

If ∠BCD = ∠CDE,

∠ACB = 180° − ∠CDE

Since ∠EDF and ∠CDE are supplementary,

180° − ∠CDE = ∠EDF

So, ∠ACB = ∠EDF.

From part a, ∠EDF = 31°.

So, ∠ACB = ∠EDF = 31°.


STA: 8m45 | 8m48 TOP: Geometry and Spatial Sense

KEY: Communication

ID: A

8

70. ANS:

Methods may vary. Sample:

∠ABC = ∠ACB = 45°

∠DCE = ∠ACB = 45°

∠CDE + ∠DCE + ∠E = 180°

∠CDE + 45° + 86° = 180°

∠CDE + 131° = 180°

∠CDE = 180° − 131°

= 49°

PTS: 1 DIF: Difficult REF: 7.2 Angles in a Triangle


71. ANS:


∠Q = ∠PRQ

∠S = ∠RPS = 28°

∠PRS + ∠S + ∠RPS = 180°

∠PRS + 28° + 28° = 180°

∠PRS + 56° = 180°

∠PRS = 180° − 56°

= 124°

∠PRQ + ∠PRS = 180°

∠PRQ + 124° = 180°

∠PRQ = 180° − 124°

= 56°

∠Q = ∠PRQ = 56°



ID: A

9

72. ANS:


Since ∆ABD is isosceles, ∠ABD = ∠ADB.

∠ABD + ∠ADB + ∠A = 180°

∠ABD + ∠ADB + 112° = 180°

∠ADB + ∠ADB + 112° = 180°

2∠ADB + 112° = 180°

2∠ADB = 180° − 112°

∠ADB =180° − 112°

2= 34°

∠ADC = ∠ABC = 90°

∠BDC is complementary to ∠ADB.

∠BDC = 90° − ∠ADB

= 90° − 34°

= 56°



73. ANS:


Since OP, OQ, and OR are radii of the same circle, OP = OQ = OR.

∆OPQ and ∆OQR are isosceles triangles.

∠P = ∠OQP = 26°

∠POQ + ∠P + ∠OQP = 180°

∠POQ + 26° + 26° = 180°

∠POQ + 52° = 180°

∠POQ = 180° − 52°

= 128°

∠QOR + ∠POQ = 180°

∠QOR + 128° = 180°

∠QOR = 180° − 128°

= 52°

Since ∆OQR is isosceles, ∠OQR = ∠R.

∠R + ∠OQR + ∠QOR = 180°

∠R + ∠OQR + 52° = 180°

∠R + ∠R + 52° = 180°

2∠R = 180° − 52°

∠R =180° − 52°

2= 64°



ID: A

10

74. ANS:


∆ACB is congruent to ∆ACD.

∠BAC = ∠CAD∠BAC + ∠CAD = ∠BAD = 44°

∠BAC + ∠CAD = 44°

∠BAC + ∠BAC = 44°

2∠BAC = 44°

∠BAC =44°

2= 22°

∠ACB + ∠BAC + ∠B = 180°

∠ACB + ∠BAC + ∠BAC = 180°

∠ACB + 22° + 22° = 180°

∠ACB + 44° = 180°

∠ACB = 180° − 44°

= 136°

∠ACD = ∠ACB∠C + ∠ACB + ∠ACD = 360°

∠C + ∠ACB + ∠ACB = 360°

∠C + 136° + 136° = 360°

∠C + 272° = 360°

∠C = 360° − 272°

= 88°



75. ANS:

Since PQ = PR, ∆PQR is isosceles.

∠PRQ = ∠Q = 79°

In ∆PQR, the sum of the angles is 180°.

∠QPR + ∠PRQ + ∠Q = 180°

∠QPR + 79° + 79° = 180°

∠QPR + 158° = 180°

∠QPR = 180° − 158°

= 22°

PS is a transversal intersecting the 2 parallel segments SR and PQ.

The interior angles ∠S and ∠QPS are supplementary.

∠S + ∠QPS = 180°

∠S + (∠QPR + 90°) = 180°

∠S + 22° + 90° = 180°

∠S + 112° = 180°

∠S = 180° − 112°

= 68°

PTS: 1 DIF: Difficult REF: 7.3 Angle Properties of Parallel Lines


ID: A

11

76. ANS:

a) ∠QBC

b) ∠Rc) ∠BQR or ∠BCR



77. ANS:

Since DE = DF, ∆DEF is isosceles.

∠E = ∠F = 45°

Since CD is parallel to EF, ∠CDE and ∠E are alternate angles.∠CDE = ∠E = 45°

Since BC is parallel to DE, ∠C and ∠CDE are alternate angles.∠C = ∠CDE = 45°

Since AB is parallel to CD, ∠B and ∠C are alternate angles.∠B = ∠C = 45°



78. ANS:

Since OA = OC, ∆OAC is isosceles.

∠ACO = ∠A = 68°

AC is parallel to OD. The alternate angles, ∠COD and ∠ACO are equal.

So, ∠COD = ∠ACO = 68°

Since OC = OD, ∆OCD is isosceles.

∠OCD = ∠DIn ∆OCD, the sum of the angles is 180°.

∠OCD + ∠D + ∠COD = 180°

∠OCD + ∠OCD + 68° = 180°

2∠OCD + 68° = 180°

2∠OCD = 180° − 68°

∠OCD =180° − 68°

2= 56°

∠ACD = ∠ACO + ∠OCD

= 68° + 56°

= 124°



ID: A

12

79. ANS:

Since ∠A and ∠ADE are alternate angles,

∠A = ∠ADE = 110°

Since AB = AD, ∆ABD is isosceles.

∠ADB = ∠ABDIn ∆ABD, the sum of the angles is 180°.

∠ABD + ∠ADB + ∠A = 180°

∠ABD + ∠ABD + 110° = 180°

2∠ABD + 110° = 180°

2∠ABD = 180° − 110°

∠ABD =180° − 110°

2

= 35°

Since ∠ABD and ∠BDC are alternate angles,

∠BDC = ∠ABD = 35°

∠BCD is complementary to ∠BDC.

∠BCD = 90° − 35°

= 55°



80. ANS:


Since OA and OB are radii of the same circle, OA = OB.

∆OAB is isosceles. So, ∠OAB = ∠ABO = 45°.

∆OBC is equilateral. So, ∠OBC = 60°.

∠ABC = ∠ABO + ∠OBC

= 45° + 60°

= 105°

PTS: 1 DIF: Difficult REF: 7.6 Creating and Solving Geometry Problems


ID: A

13

81. ANS:


Since ∆ABC is equilateral, ∠B = 60°.

Since ∠BAD = 90°, ∠ADB is complementary to ∠B.

So, ∠ADB = 90° − 60° = 30°.

∠ADE is supplementary to ∠ADB.

So, ∠ADE = 180° − 30° = 150°.

Since AD = DE, ∆ADE is isosceles.

So, ∠DAE = ∠AED.

The sum of angles in a triangle is 180°.

∠DAE + ∠AED + ∠ADE = 180°

x + x + 150° = 180°

2x = 180° + 150°

x = 15°



82. ANS:


BQ is parallel to SR. ∠QBC and ∠RCD are corresponding angles along transversal AD.

∠QBC = ∠RCD = 70°

∠PBQ = 180° − 55° − 70° = 55°

QC is parallel to PS. ∠Q and ∠PBQ are alternate angles along transversal BQ.

∠Q = ∠PBQ = 55°



83. ANS:

Since AB = AC, ∆ABC is isosceles.

So, ∠B = ∠C = 74°.


∠BAC + ∠B + ∠C = 180°

∠BAC + 74° + 74° = 180°

∠BAC = 180° − 2 × 74°

= 32°

∠BAC and ∠ACD are alternate angles along transversal CA.

So, ∠ACD = ∠BAC = 32°

∠D is complementary to ∠ACD.

So, ∠D = 90° − ∠ACD

= 90° − 32°

= 58°



ID: A

14

84. ANS:


∠Q and ∠QLM are alternate angles along transversal QL.

So, ∠Q = ∠QLM = 30°


∠PLQ + ∠LPQ + ∠Q = 180°

∠PLQ + 44° + 30° = 180°

∠PLQ = 180° − 44° − 30°

= 106°

∠KPL and ∠PLQ are alternate angles along transversal PL.

∠KPL = ∠PLQ = 106°

∠KPQ = ∠KPL + ∠PLQ

= 44° + 106°

= 150°



chapter 7 test, review

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