The Polygon Angle-Sum Theorems

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Presentation transcript:

The Polygon Angle-Sum Theorems GEOMETRY LESSON 3-4 12. 1800 13. 1440 14. 3240 15. 180,000 16. 102 17. 103 18. 145 19. 37 Pages 147-150 Exercises 1. yes 2. No; it has no sides. 3. No; it is not a plane figure. 4. No; two sides intersect between endpoints. 5. MWBFX; sides: MW, WB, BF, FX, XM ; : M, W, B, F, X s 6. KCLP; sides: KC, CL, LP, PK; : K, C, L, P 7. HEPTAGN; sides: HE, EP, PT, TA, AG, GN, NH; : H, E, P, T, A, G, N 8. pentagon; convex 9. decagon; concave 10. pentagon; concave 11. 1080 3-4

The Polygon Angle-Sum Theorems GEOMETRY LESSON 3-4 20. 60, 60, 120, 120 21. 113, 119 22. 108; 72 23. 150; 30 24. 160; 20 25. 176.4; 3.6 26. 45, 45, 90 27. 28. 29. 30. 31. 32. 3 33. 8 34. 13 35. 18 36. a. 3; 6 b. 4; 8 c. 5; 10 3-4

The Polygon Angle-Sum Theorems GEOMETRY LESSON 3-4 37. octagon; m 1 = 135; m 2 = 45 38. If you solve = 130, you get n = 7.2. This number is not an integer. 39. 20-80-80; 50-50-80 40. 108; 5 41. 144; 10 42. 162; 20 (n – 2) 180 n 43. 150; 12 44. 180 – x; 45. 46. a. n • 180 b. (n – 2)180 c. 180n – 180(n – 2) = 360 d. Polygon Ext. -Sum Thm. 47. y = 103; z = 70; quad. 360 x 4 5 48. w = 72, x = 59, y = 49, z = 121; 49. x = 36, 2x = 72, 3x = 108, 4x = 144; quad. 50–53. Answers may vary. Samples are given 50. 51. 3-4

The Polygon Angle-Sum Theorems GEOMETRY LESSON 3-4 52. 53. 54. Yes; the sum of the measures of at the int. point is 360. The sum of the measures of all the is 180n. 180n – 360 = (n – 2)180 55. Answers may vary. Sample: The figure is a convex equilateral quad. The sum of its is 2 • 180 or 360. 56. octagon 57. a. (20, 162), (40, 171), (60, 174), (80,175.5), (100, 176.4), (120, 177), (140, 177.4), (160, 177.75), (180, 178), (200, 178.2) b. c. It is very close to 180 d. No, two sides cannot be collinear. s s s 3-4

The Polygon Angle-Sum Theorems GEOMETRY LESSON 3-4 180n – 360 n 360 n 58. a. [180(n – 2)] ÷ n = = 180 – . b. As n gets larger, the size of the angles get closer to 180. The more sides it has, the closer the polygon is to a circle. 59. 36 60–63. Answers may vary. Samples are given. 60. 61. Not possible; opp. sides would overlap. 62. 63. Not possible; opp. and adj. sides would overlap. 64. 4140 65. 20 66. 225 67. 360 68. 157.5 3-4

The Polygon Angle-Sum Theorems GEOMETRY LESSON 3-4 69. 27 70. 10 71. 120, 25 72. 50, 40 73. 104, 76, 35, 69 74. Distr. Prop. 75. Subst. Prop. 76. Reflexive Prop. of 77. Symm. Prop. of 78. Div. Prop. 79. Trans. Prop. 80. RT, RK 81. BRT, BRK 82. Answers may vary. Sample: BR and TK. 83. Answers may vary. Sample: BRM 84. TRM 85. TRK 86. R 3-4