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Angle Relationships & Parallel Lines

Angle Relationships & Parallel Lines. Pre-Algebra. www.ih.k12.oh.us/MSDunlap/Geometry/Angle%20Relationships.ppt. Adjacent angles are “side by side” and share a common ray. 15 º. 45 º. These are examples of adjacent angles. 45 º. 80 º. 35 º. 55 º. 130 º. 50 º. 85 º. 20 º.

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Angle Relationships & Parallel Lines

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  1. Angle Relationships&Parallel Lines Pre-Algebra www.ih.k12.oh.us/MSDunlap/Geometry/Angle%20Relationships.ppt

  2. Adjacent angles are “side by side” and share a common ray. 15º 45º

  3. These are examples of adjacent angles. 45º 80º 35º 55º 130º 50º 85º 20º

  4. These angles are NOT adjacent. 100º 50º 35º 35º 55º 45º

  5. Complementary Anglessum to 90° 50° 40°

  6. Complementary angles add up to 90º. 30º 40º 50º 60º Adjacent and Complementary Angles Complementary Anglesbut not Adjacent

  7. Supplementary Anglessum to 180° 150° 30°

  8. Supplementary angles add up to 180º. 40º 120º 60º 140º Adjacent and Supplementary Angles Supplementary Anglesbut not Adjacent

  9. Vertical Anglesare opposite one another.Vertical angles are congruent. 100° 100°

  10. Vertical Anglesare opposite one another.Vertical angles are congruent. 80° 80°

  11. Lines l and m are parallel.l||m Note the 4 angles that measure 120°. 120° 120° l 120° 120° m Line n is a transversal. n

  12. Lines l and m are parallel.l||m Note the 4 angles that measure 60°. 60° 60° l 60° 60° m Line n is a transversal. n

  13. Lines l and m are parallel.l||m There are 4 pairs of angles that are vertical. There are many pairs of angles that are supplementary. 60° 120° 120° 60° l 60° 120° 120° 60° m Line n is a transversal. n

  14. If two lines are intersected by a transversal and any of the angle pairs shown below are congruent, then the lines are parallel. This fact is used in the construction of parallel lines.

  15. Practice Time!

  16. 1) Find the missing angle. ?° 36°

  17. 1) Find the missing angle. ?° 36° 90 ° – 36 = 54°

  18. 2) Find the missing angle. ?° 64°

  19. 2) Find the missing angle. ?° 64° 90 ° – 64° = 26°

  20. 3) Solve for x. 2x° 3x°

  21. 3) Solve for x. 2x° 3x° 3x° + 2x° = 90° 5x = 90 x =18

  22. 4) Solve for x. x + 25 2x + 5

  23. 4) Solve for x. x + 25 2x + 5 (2x + 5) + (x + 25) = 90 3x + 30 = 90 3x = 60 x = 20

  24. 5) Find the missing angle. 168° ?°

  25. 5) Find the missing angle. 168° ?° 180° – 168° = 12°

  26. 6) Find the missing angle. ?° 58°

  27. 6) Find the missing angle. ?° 58° 180° – 58° = 122°

  28. 7) Solve for x. 5x 4x

  29. 7) Solve for x. 5x 4x 4x + 5x = 180 9x = 180 x = 20

  30. 8) Solve for x. 3x + 20 2x + 10

  31. 8) Solve for x. 3x + 20 2x + 10 (2x + 10) + (3x + 20) = 180 5x + 30 = 180 5x = 150 x = 30

  32. 9) Lines l and m are parallel.l||mFind the missing angles. 42° a ° c° b° l d° e° g° f° m

  33. 9) Lines l and m are parallel.l||mFind the missing angles. 42° 138° 138° 42° l 42° 138° 138° 42° m

  34. 10) Lines l and m are parallel.l||mFind the missing angles. 81° a ° c° b° l d° e° g° f° m

  35. 10) Lines l and m are parallel.l||mFind the missing angles. 81° 99° 99° 81° l 81° 99° 99° 81° m

  36. 11) Find the missing angles. 70 ° 70 ° b° Hint: The 3 angles in a triangle sum to 180°. d ° 65 °

  37. 11) Find the missing angles. 70 ° 70 ° 40° Hint: The 3 angles in a triangle sum to 180°. 75 ° 65 °

  38. 12) Find the missing angles. 45 ° 50 ° b° Hint: The 3 angles in a triangle sum to 180°. d ° 75 °

  39. 12) Find the missing angles. 45 ° 50 ° 85° Hint: The 3 angles in a triangle sum to 180°. 20° 75 °

  40. In the figure a || b. 13. Name the angles congruent to 3. 1, 5, 7 14. Name all the angles supplementary to 6. 1, 3, 5, 7 15. If m1 = 105° what is m3? 105° 16. If m5 = 120° what is m2? 60°

  41. The End Sources www.ih.k12.oh.us/MSDunlap/Geometry/Angle%20Relationships.ppt

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