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Angle relationships

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Transcript

  • 1. Angle Relationships & Parallel Lines Pre-Algebra
  • 2. Adjacent angles are “side by side” and share a common ray. 15º 45º
  • 3. These are examples of adjacent angles. 80º 45º 35º 55º 130º 50º 85º 20º
  • 4. These angles are NOT adjacent. 100º 50º 35º 35º 55º 45º
  • 5. Complementary Angles sum to 90° 50° 40°
  • 6. Complementary angles add up to 90º. 30º 40º 50º 60º Adjacent and Complementary Complementary Angles Angles but not Adjacent
  • 7. Supplementary Angles sum to 180° 30° 150°
  • 8. Supplementary angles add up to 180º. 40º 120º 60º 140º Adjacent and Supplementary Supplementary Angles Angles but not Adjacent
  • 9. Vertical Angles are opposite one another.Vertical angles are congruent. 100° 100°
  • 10. Vertical Angles are 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° mLine 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° mLine n is a transversal. n
  • 13. Lines l and m are parallel. l||mThere are many There are 4 pairs ofpairs of angles that angles that areare supplementary. vertical. 60° 120° 120° 60° l 60° 120° 120° 60° m Line n is a transversal. n
  • 14. If two lines are intersected by a transversaland any of the angle pairs shown below arecongruent, then the lines are parallel. Thisfact is used in the construction of parallellines.
  • 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. 4x 5x
  • 29. 7) Solve for x. 4x 5x 4x + 5x = 180 9x = 180 x = 20
  • 30. 8) Solve for x. 2x + 10 3x + 20
  • 31. 8) Solve for x. 2x + 10 3x + 20 (2x + 10) + (3x + 20) = 180 5x + 30 = 180 5x = 150 x = 30
  • 32. 9) Lines l and m are parallel. l||m Find the missing angles. 42° a° c° b° l d° e° g° f° m
  • 33. 9) Lines l and m are parallel. l||m Find the missing angles. 42° 138° 138° 42° l 42° 138° 138° 42° m
  • 34. 10) Lines l and m are parallel. l||m Find the missing angles. 81° a° c° b° l d° e° g° f° m
  • 35. 10) Lines l and m are parallel. l||m Find 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 atriangle sum to 180°. d° 65 °
  • 37. 11) Find the missing angles. 70 ° 70 ° 40°Hint: The 3 angles in atriangle sum to 180°. 75 ° 65 °
  • 38. 12) Find the missing angles. 45 ° 50 ° b°Hint: The 3 angles in atriangle sum to 180°. d° 75 °
  • 39. 12) Find the missing angles. 45 ° 50 ° 85°Hint: The 3 angles in atriangle sum to 180°. 20° 75 °
  • 40. In the figure a || b.13. Name the angles congruent to ∠3. ∠1, ∠5, ∠714. Name all the angles supplementary to ∠6. ∠1, ∠3, ∠5, ∠715. If m∠1 = 105° what is m∠3? 105°16. If m∠5 = 120° what is m∠2? 60°
  • 41. The End

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