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AnglesAngles: CLASSWORKClassify each angle using all of the names that apply: acute, right, obtuse, straight, or reflex.1. 2. 3.

Determine if each statement below is always, sometimes, or never true.4. An angle that measures 90 degrees is ____________ an acute angle.5. An angle that is more than 90 degrees is _____________ obtuse.6. The interior of an angle is ______________ located outside of the angle.7. An obtuse angle is _____________ considered to be a reflex angle.

Angles: HOMEWORK8. 9. 10.

Determine if each statement below is always, sometimes, or never true.11. An obtuse angle is ____________ considered to be a straight angle.12. An angle that is less than 90 degrees is _____________ straight.13. The exterior of an angle is ______________ located outside of the angle.14. A reflex angle is _____________ considered to be an obtuse angle.

Congruent Angles: CLASSWORKDetermine if each pair of angles are congruent. If so, write a congruence statement. If not, explain why.15. 16. 17.

Congruent Angles: HOMEWORKDetermine if each pair of angles are congruent. If so, write a congruence statement. If not, explain why.18. 19. 20.

Geometry - Angles ~1~ NJCTL.org

Angles & Angle Addition Postulate: CLASSWORK – For #21-25, find the missing angle measure.


21. 22.23.

24. 25.

26. 27.

28.

Angles & Angle Addition Postulate: HOMEWORK – For #29-33, find the missing angle measure.


PARCC-type question:37. The figure shows the lines h, k, j, and ray g intersecting to form the angles numbered 1, 2, 3, 4, 5, 6, and 7. All of the lines and ray are in the same plane. Based on the figure, which of the individual statements would provide enough information to concluded that line k is perpendicular to line j? Circle all that apply.

Protractors: CLASSWORK

Use the figure above to find the measurement of each angle.

Protractors: HOMEWORKUse the figure above to find the measurement of each angle.


34.

35.

36.

29. 30.

31.

32.

33.

Figure for #38 - 49

Special Angle Pairs: CLASSWORK 50. True/False: Complementary angles form a right angle

51. True/False: Supplementary angles form a straight angle

52. Two angles are complementary. One of the angles is 17°, what is the measure of the other angle?

53. Two angles are supplementary. One of the angles is 97°, what is the measure of the other angle?

54. Two angles are supplementary. One of the angles is three times the size of the other, what is the measure of the larger angle?

55. An angle x is 20° more than its complement. What is the angle’s measure?

56. An angle x is 66° less than its complement. What is the angle’s measure?

57. An angle x is 46° more than its supplement. What is the angle’s measure?

58. An angle x is 18° less than its supplement. What is the angle’s measure?

Special Angle Pairs: HOMEWORK 59. True/False: Supplementary angles always sum to 90°

60. True/False: Complementary angles sometimes form straight angles

61. Two angles are complementary. One of the angles is 57°, what is the measure of the other angle?

62. Two angles are supplementary. One of the angles is 43°, what is the measure of the other angle?

63. Two angles are supplementary. One of the angles is five times the smaller angle, what is the measure of the larger angle?

64. An angle is 74° more than its complement. What is the angle’s measure?

65. An angle is 36° less than its complement. What is the angle’s measure?

66. An angle is 88° more than its supplement. What is the angle’s measure?

67. An angle is 16° less than its supplement. What is the angle’s measure?


Proofs of Special Angles: CLASSWORKFind the measures of the missing angles.68. 69.

Find the value of the variables.70. 71. 72.

73. 74. 75.


Proofs of Special Angles: HOMEWORKFind the measures of the missing angles.76. 77.

Find the value of x.78. 79. 80.

81. 82. 83.


Angle Bisector: CLASSWORKGiven that ray BD bisects ∠ ABC in the figure below, find the missing measurements. Note: the questions are NOT related.

Given that ray JL bisects ∠ IJK in the figure below, find the value of x.88. 89.

90. 91.


84. 85.

86. 87.

Angle Bisector: HOMEWORK Given that ray RT bisects ∠ QRS in the figure below, find the missing measurements. Note: the questions are NOT related.

Given that ray JL bisects ∠ IJK in the figure below, find the value of x.96. 97.

98. 99.


92. 93.

94. 95.

Locus & Angle Constructions: CLASSWORK 10. Construct a congruent angle for each figure below. a)

b)

Locus & Angle Constructions: HOMEWORK 101. Construct a congruent angle for each figure below. a)

b)


Angle Bisectors & Constructions: CLASSWORK 102. Construct the angle bisector of each angle below using any construction method of your choice. a) b)

Angle Bisectors & Constructions: HOMEWORK 103. Construct the angle bisector of each angle below using any construction method of your choice. a) b)

PARCC type question:104. The figure below shows angle NOP.

Part A:

Consider the partial construction of a ray that would bisect angle NOP. What would be the final step in the construction? a) Draw a ray starting at point P going through point T.b) Draw a ray starting at point N going through point T.c) Draw a ray starting at point O going through point T.d) Draw a ray starting at point R going through point T.

Part B:Once the construction is complete, which of the following reasons listed contribute to providing the validity of the construction?


AnglesReview Multiple Choice

105. Opposite rays (circle all that apply):a.are collinearb.have the same endpointc.sometimes overlapd.form a straight angle

106. Two rays that have a common endpoint could form (check all that apply):a. an angleb. a straight linec. opposite raysd. a vertex

107. Acute angles are:a. less than 90°b. greater than 90° but less than 180°c. equal to 180°d. greater than 180° but less than 360°

108. Obtuse angles are:a. less than 90°b. greater than 90° but less than 180°c. equal to 180°d. greater than 180° but less than 360°

109. Adjacent angles (circle all that apply):a. have a common sideb. sum to 90°c. share a common vertexd. are less than 90°

110. Complementary angles (circle all that apply):a. sum to 90°b. sum to 180°c. form a straight angled. form a right anglee. are adjacent angles

111. Supplementary angles (circle all that apply):a. sum to 90°b. sum to 180°c. form a straight angled. form a right anglee. are adjacent angles


112. An angle measures 34°. What is the measure of its supplement?a. 56°b. 66°c. 156°d. 146°

113. An angle measures 58°. What is the measure of its complement?a. 22°b. 32°c. 42°d. 122°

114. Find the measures of the angles to the right. a.b.c.d.

115. Find the value of x in the figure to the right.a. ½ b. 9c. 12d. 24

116. An angle bisector (circle all that apply):a. forms two congruent anglesb. is a line or a rayc. is equidistant from the sides of the angled. forms two adjacent angles

117. The statement, "the whole is the sum of the parts" refers to (circle all that apply):a. complementary anglesb. the segment addition postulatec. adjacent anglesd. the angle addition postulate

118. Ray RT bisects ∠QRS. If m∠QRT = 33°, what are the measurements of the remaining two angles? a. m∠TRS = 33°, m∠QRS = 33° b. m∠TRS = 66°, m∠QRS = 66°c. m∠TRS = 33°, m∠QRS = 66°d. m∠TRS =66°, m∠QRS = 33°

119. Ray OL bisects ∠NOP. Find the value of x. a. 2b. 4.8c. 6.5d. 9


120. The figure shows the o, p, and q intersecting to form the angles numbered 1, 2, 3, 4, 5, and 6. All of the lines are in the same plane. Based on the figure, which of the individual statements would provide enough information to concluded that line o is perpendicular to line q? Circle all that apply.

121. The figure below shows angle ACE.

Part A:

Consider the partial construction of a ray that would bisect angle ACE. What would be the final step in the construction?

a. Draw a ray starting at point D going through point F.b. Draw a ray starting at point C going through point F.c. Draw a ray starting at point B going through point F.d. Draw a ray starting at point A going through point F.

Part B:Once the construction is complete, which of the following reasons listed contribute to providing the validity of the construction?


AnglesReview Constructed Response

122. An angle is 36° less than its complement. What is the measure of the angle?

123. An angle is 102° more than its supplement. What is the measure of the angle?

124. If F is in the interior of ∠APB and m∠APB = (5x +11)°, m∠APF = (6x – 6)° and m∠FPB = (9x – 23)°: Draw a diagram Solve for x What is the m∠FPB, m∠APF and m∠APB?


Answer Key1. Acute2. Obtuse, straight3. Obtuse, reflex4. Never5. Always6. Never7. Sometimes8. Right9. Obtuse10. Obtuse, reflex11. Sometimes12. Never13. Always14. Always15. Yes ∠BCD ≅ ∠EFG16. No; angle measures are

not equal17. No; not enough info18. No; not enough info19. Yes; ∠TUV ≅ ∠WXY20. No; angle measures are

not equal21. 26°22. 72°23. 23°24. 123°25. 193°26. 1527. 328. 329. 71°30. 14°31. 17°32. 57°33. 33°

34. 5.8666...35. 236. 737. b & d38. 30°39. 180°40. 155°41. 90°42. 107°43. 120°44. 97°45. 25°46. 150°47. 83°48. 72°49. 72°50. True51. True52. 73°53. 83°54. 135°55. 55°56. 12°57. 113°58. 81°59. False60. False61. 33°62. 137°63. 150°64. 82°65. 27°66. 134°67. 82°68. 63°, 117°, 63°69. 128°, 128°, 52°

70. x = 1771. x = 772. x = 1673. x = 1374. x = 16 & y = 675. x = 4 & y = 676. 126°, 54°, 54°77. 147°, 147°, 33°78. x = 1179. x = 780. x = 1381. x = 1082. x = 20 & y = 583. x = 10 & y = 2084. 39°, 39°85. 44°, 44°86. 112°, 56°87. 46°, 92°88. x = 2489. x = 690. x = 1091. x = 992. 48°, 96°93. 88°, 176°94. 83°, 83°95. 53°, 53°96. x = 1097. x = 2198. x = 899. x = 4.5100. Check

Constructions101. Check Constructions102. Check Constructions103. Check Constructions104. Part A: c

Part B: d

Review Answer Key Multiple Choice105. A, B, D106. A, B, C, D107. A108. B109. A, C110. A, D111. B, C112. D113. B

114. C115. D116. A, B, C, D117. B, D118. C119. D120. B, D121. Part A: B

Part B: A

16

Review Answer Key Constructed Response

122. x = 27°

123. x = 141°

124.x = 4m∠FPB = 13°m∠APF = 18°m∠APB = 31°

m∠APF = 18⁰

m∠APB = 31⁰

17

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