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Angles Angles: CLASSWORK Classify each angle using all of the names that apply: acute, right, obtuse, straight, or reflex. 1. 2. 3. I 16° 180° Y X K J Z U V 240° W 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: HOMEWORK 8. 9. O 10. L R 90° 120° P Q S N M 344° T 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: CLASSWORK Determine if each pair of angles are congruent. If so, write a congruence statement. If not, explain why. 15. 16. 17. B H C E F I D 52° K J L G F Z E 51° M B D A Congruent Angles: HOMEWORK Determine if each pair of angles are congruent. If so, write a congruence statement. If not, explain why. 18. 19. 20. N T Q R S Geometry - Angles O P U 60° V X ~1~ J E W 60° Y F G H I NJCTL.org Angles & Angle Addition Postulate: CLASSWORK – For #21-25, find the missing angle measure. 21. #106 22. #107 24.#109 25. #110 26. 111. 23.#108 27. 112. 28. 113. Geometry - Angles ~2~ NJCTL.org Angles & Angle Addition Postulate: HOMEWORK – For #29-33, find the missing angle measure. 29. 30. 31. 32. 34. 33. 35. 36. Geometry - Angles ~3~ NJCTL.org 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. h k 7 6 g 12 3 54 a. b. c. d. e. f. mÐ3 + mÐ4 = 90° mÐ3 = 90° mÐ1 + mÐ7 = 90° mÐ6 + mÐ7 = 90° mÐ1 = mÐ4 mÐ4 = 90° j Protractors: CLASSWORK Figure for #38 - 49 Use the figure above to find the measurement of each angle. 38. mÐAHB = 39. mÐAHG = 40. mÐAHF = 41. mÐBHE = 42. mÐCHF = 43. mÐDHE = Protractors: HOMEWORK Use the figure above to find the measurement of each angle. 44. mÐAHE = 45. mÐFHG = 46. mÐBHG = 47. mÐAHD = 48. mÐCHE = 49. mÐDHF = Geometry - Angles ~4~ NJCTL.org 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? Geometry - Angles ~5~ NJCTL.org Proofs of Special Angles: CLASSWORK Find the measures of the missing angles. 68. 69. Find the value of the variables. 70. 71. 72. 73. 74. 75. Geometry - Angles ~6~ NJCTL.org Proofs of Special Angles: HOMEWORK Find the measures of the missing angles. 76. 77. 33° 4 5 6 Find the value of x. 78. 79. 80. 81. 82. 83. Geometry - Angles ~7~ NJCTL.org Angle Bisector: CLASSWORK Given that ray BD bisects ∠ ABC in the figure below, find the missing measurements. Note: the questions are NOT related. 84. 85. 86. 87. Given that ray JL bisects ∠ IJK in the figure below, find the value of x. 88. 89. 90. 91. Geometry - Angles ~8~ NJCTL.org Angle Bisector: HOMEWORK Given that ray RT bisects ∠ QRS in the figure below, find the missing measurements. Note: the questions are NOT related. 93. 92. R Q S 94. 95. T Given that ray JL bisects ∠ IJK in the figure below, find the value of x. 96. 97. 98. 99. Geometry - Angles ~9~ NJCTL.org Locus & Angle Constructions: CLASSWORK 10. Construct a congruent angle for each figure below. a) A B C b) D E F Locus & Angle Constructions: HOMEWORK 101. Construct a congruent angle for each figure below. a) H G I b) K J L Geometry - Angles ~10~ NJCTL.org 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. 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. N O P Part A: Part B: Once the construction is complete, which of the following reasons listed contribute to providing the validity of the construction? N T Q O R Geometry - Angles a) b) c) d) P ~11~ mÐNQT = mÐNOP mÐQNT = mÐNOP mÐTRP = mÐNOP mÐNOT = mÐPOT NJCTL.org Angles Review Multiple Choice 105. Opposite rays (circle all that apply): a.are collinear b.have the same endpoint c.sometimes overlap d.form a straight angle 106. Two rays that have a common endpoint could form (check all that apply): a. an angle b. a straight line c. opposite rays d. 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 side b. sum to 90° c. share a common vertex d. are less than 90° 110. Complementary angles (circle all that apply): a. sum to 90° b. sum to 180° c. form a straight angle d. form a right angle e. are adjacent angles 111. Supplementary angles (circle all that apply): a. sum to 90° b. sum to 180° c. form a straight angle d. form a right angle e. are adjacent angles Geometry - Angles ~12~ NJCTL.org 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. 1 113° 2 3 115. Find the value of x in the figure to the right. a. ½ b. 9 (x+19)° c. 12 d. 24 (5x+17)° 116. An angle bisector (circle all that apply): a. forms two congruent angles b. is a line or a ray c. is equidistant from the sides of the angle d. forms two adjacent angles 117. The statement, "the whole is the sum of the parts" refers to (circle all that apply): a. complementary angles b. the segment addition postulate c. adjacent angles d. 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° T c. m∠TRS = 33°, m∠QRS = 66° Q d. m∠TRS =66°, m∠QRS = 33° 119. Ray OL bisects ∠NOP. Find the value of x. a. 2 N b. 4.8 c. 6.5 (5x + 16)° d. 9 O Geometry - Angles ~13~ R S L (8x - 11)° P NJCTL.org 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. p q 1 23 6 54 o 121. a. b. c. d. e. f. mÐ3 + mÐ4 = 90° mÐ3 = 90° mÐ5 + mÐ6 = 90° mÐ4 + mÐ5 = 90° mÐ3 = mÐ6 mÐ4 = 90° The figure below shows angle ACE. A C E Part A: A F B C D E 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? a. mÐACF = mÐECF b. mÐABF = mÐACE c. mÐFDE = mÐACE d. mÐACE = mÐBAF Geometry - Angles ~14~ NJCTL.org Angles Review 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? Geometry - Angles ~15~ NJCTL.org Answer Key 1. Acute 2. Obtuse, straight 3. Obtuse, reflex 4. Never 5. Always 6. Never 7. Sometimes 8. Right 9. Obtuse 10. Obtuse, reflex 11. Sometimes 12. Never 13. Always 14. Always 15. Yes ∠BCD ≅ ∠EFG 16. No; angle measures are not equal 17. No; not enough info 18. No; not enough info 19. Yes; ∠TUV ≅ ∠WXY 20. No; angle measures are not equal 21. 26° 22. 72° 23. 23° 24. 123° 25. 193° 26. 15 27. 3 28. 3 29. 71° 30. 14° 31. 17° 32. 57° 33. 33° 34. 5.8666... 105. 106. 107. 108. 109. 110. 111. 112. A, B, D A, B, C, D A B A, C A, D B, C D Geometry - Angles 35. 2 36. 7 37. b & d 38. 30° 39. 180° 40. 155° 41. 90° 42. 107° 43. 120° 44. 97° 45. 25° 46. 150° 47. 83° 48. 72° 49. 72° 50. True 51. True 52. 73° 53. 83° 54. 135° 55. 55° 56. 12° 57. 113° 58. 81° 59. False 60. False 61. 33° 62. 137° 63. 150° 64. 82° 65. 27° 66. 134° 67. 82° 68. 63°, 117°, 63° 69. 128°, 128°, 52° 70. x = 17 71. x = 7 72. x = 16 73. x = 13 74. x = 16 & y = 6 75. x = 4 & y = 6 76. 126°, 54°, 54° 77. 147°, 147°, 33° 78. x = 11 79. x = 7 80. x = 13 81. x = 10 82. x = 20 & y = 5 83. x = 10 & y = 20 84. 39°, 39° 85. 44°, 44° 86. 112°, 56° 87. 46°, 92° 88. x = 24 89. x = 6 90. x = 10 91. x = 9 92. 48°, 96° 93. 88°, 176° 94. 83°, 83° 95. 53°, 53° 96. x = 10 97. x = 21 98. x = 8 99. x = 4.5 100. Check Constructions 101. Check Constructions 102. Check Constructions 103. Check Constructions 104. Part A: c Part B: d Review Answer Key Multiple Choice 113. B 114. C 115. D 116. A, B, C, D 117. B, D 118. C 119. D 120. B, D ~16~ NJCTL.org 121. Part A: B Part B: A Review Answer Key Constructed Response 122. x = 27° 123. x = 141° 124. x=4 m∠FPB = 13° m∠APF = 18° m∠APB = 31° Geometry-PLPA ~17~ NJCTL.org