Parallel Lines and the Triangle Angle-Sum Theorem GEOMETRY LESSON 3-3 Pages 135-139 Exercises 1. 30 2. 83.1 3. 90 4. 71 5. 90 6. x = 70; y = 110; z = 30 7. t = 60; w = 60 8. x = 80; y = 80 9. 70 10. 30 11. 60 12. acute, isosceles 13. acute, equiangular, equilateral 14. right, scalene 15. obtuse, isosceles 16. 17. Not possible; a right will always have one longest side opp. the right . 18. 3-3

Parallel Lines and the Triangle Angle-Sum Theorem GEOMETRY LESSON 3-3 19. 20. 21. 22. 23. 24. a. 5, 6, 8 b. 1 and 3 for 5 1 and 2 for 6 1 and 2 for 8 c. They are vert. . 25. a. 2 b. 6 26. 123 s 27. 115.5 28. m 3 = 92; m 4 = 88 29. x = 147, y = 33 30. a = 162, b = 18 31. x = 52.5; 52.5, 52.5, 75; acute 32. x = 7; 55, 35, 90; right 33. x = 37; 37, 65, 78; acute 3-3

Parallel Lines and the Triangle Angle-Sum Theorem GEOMETRY LESSON 3-3 34. x = 38, y = 36, z = 90; ABD: 36, 90, 54; right; BCD: 90, 52, 38; right; ABC: 74, 52, 54; acute 35. a = 67, b = 58, c = 125, d = 23, e = 90; FGH: 58, 67, 55; acute; FEH: 125, 32, 23; obtuse; EFG: 67, 23, 90; right 36. x = 32, y = 62, z = 32, w = 118; ILK: 118, 32, 30; obtuse 37. 60; 180  3 = 60 38. Yes, an equilateral is isosc. Because if three sides of a are , then at least two sides are . No, the third side of an isosc. does not need to be to the other two. 39. eight 40. 32.5 3-3

Parallel Lines and the Triangle Angle-Sum Theorem GEOMETRY LESSON 3-3 41. Check students’ work. Answers may vary. Sample: The two ext. Formed at vertex A are vert. and thus have the same measure. 42. 30 and 60 43. a. 40, 60, 80 b. acute 44. 160 45. 100 s 46. 103 47. 32 48. a. 90 b. 180 c. 90 d. compl. e. compl. 49. a. Add. b. -Sum c. Trans. d. Subtr. s 50. 132; since the missing is 68, the largest ext. Is 180 – 48 = 132. 51. Check students’ work. 52. a. 81 b. 45, 63, 72 c. acute 53. 120 or 60 54. 135 or 45 55. 90 3-3

Parallel Lines and the Triangle Angle-Sum Theorem GEOMETRY LESSON 3-3 56. Greater than, because there are two with measure 90 where the meridians the equator. 57. 58. 59. 1 60. 61. 0 62. 115 s 1 3 7 19 63. Answers may vary. Sample: The measure of the ext. is = to the sum of the measures of the two remote int. . Since these are , the formed by the bisector of the ext. are to each of them. Therefore, the bisector is || to the included side of the remote int. by the Conv. of the Alt Int. Thm. 64. B 65. G 66. B 67. H s 3-3

Parallel Lines and the Triangle Angle-Sum Theorem GEOMETRY LESSON 3-3 68. [2] a. b. The correct equation is 2x = (2x – 40) + (x – 15) with the sol. x = 55. The three int. measure 70, 40, and 70. [1] incorrect sketch, equation, OR solution 69. [2] a. 159; the sum of the three of the is 180, so m Y + m M + m F = 180. Since m F = 21, m Y + m M + 21 = 180. Subtr. 21 from both sides results in m Y + m M = 159. 69. (continued) b. 1 to 68 ; since Y is obtuse, its whole number range is from 91 to 158, allowing the measure of 1 for m M when m Y = 158. When m Y = 91, then m M = 68. [1] incorrect answer to part (a) or (b) OR incorrect computation in either part s s 3-3

Parallel Lines and the Triangle Angle-Sum Theorem GEOMETRY LESSON 3-3 70. 53 71. 46 72. 7 73. 74. 3-3