14. AB // DE 36. 2 and 7 15. AB and CF 37. 1 and 5 16. BD  DF 38. transv.: l; corr. s 17. Plane ABC // plane DEF 39. transv.: n; alt. int. s 18. 2 and 6 40. transv.: m; alt. ext. s 19. 1 and 8 41. lines are skew 20. 1 and 6 44. B 45. G 46. C 21. 2 and 5 47. F 48. D 22. transv.: p; corr s 58. C = 502.7 cm; A = 20,106.2 cm2 23. transv.: q; alt. int. s 59. C = 11.9 m; A = 11.3 m2 24. transv.: l; alt. ext. s 60. Rt s  or vert s  25. transv.: p; same-side int. s 61. Linear Pair Theorem 27. corr s 62. Vert s  28. alt. int. s 29. same-side int. s 35. 8 and 5

Warm Up Identify each angle pair. 1. 1 and 3 2. 3 and 6 3. 4 and 5 4. 6 and 7 corr. s alt. int. s alt. ext. s same-side int s

Example 1 Find mQRS. x = 118 mQRS + x = 180° mQRS = 180° – x = 180° – 118° = 62°

Example 2: Music Application Find x and y in the diagram. By the Alternate Interior Angles Theorem, (5x + 4y)° = 55°. By the Corresponding Angles Postulate, (5x + 5y)° = 60°. 5x + 5y = 60 –(5x + 4y = 55) y = 5 Subtract the first equation from the second equation. Substitute 5 for y in 5x + 5y = 60. Simplify and solve for x. 5x + 5(5) = 60 x = 7, y = 5

Geometry 3.2 Angles Formed by Parallel Lines and Transversals Example 3 Find the measures of the acute angles in the diagram. By the Alternate Exterior Angles Theorem, (25x + 5y)° = 125°. By the Corresponding Angles Postulate, (25x + 4y)° = 120°. An acute angle will be 180° – 125°, or 55°. The other acute angle will be 180° – 120°, or 60°.