Angle relationships

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Angle relationships

  1. 1. Angle Relationships&Parallel LinesPre-Algebra
  2. 2. Adjacent angles are “side by side” andshare a common ray.45º15º
  3. 3. These are examples of adjacent angles.55º35º50º130º80º 45º85º20º
  4. 4. These angles are NOT adjacent.45º55º50º100º35º35º
  5. 5. Complementary Anglessum to 90°40°50°
  6. 6. Complementary angles add up to 90º.60º30º40º50ºAdjacent and ComplementaryAnglesComplementary Anglesbut not Adjacent
  7. 7. Supplementary Anglessum to 180°30° 150°
  8. 8. Supplementary angles add up to 180º.60º120º40º140ºAdjacent and SupplementaryAnglesSupplementary Anglesbut not Adjacent
  9. 9. Vertical Anglesare opposite one another.Vertical angles are congruent.100°100°
  10. 10. Vertical Anglesare opposite one another.Vertical angles are congruent.80°80°
  11. 11. Lines l and m are parallel.l||m120°lm120°120°120°Note the 4angles thatmeasure 120°.nLine n is a transversal.
  12. 12. Lines l and m are parallel.l||m60°lm60°60°60°Note the 4angles thatmeasure 60°.nLine n is a transversal.
  13. 13. Lines l and m are parallel.l||m60°lm60°60°60°There are manypairs of angles thatare supplementary.There are 4 pairs ofangles that arevertical.120°120°120°120°nLine n is a transversal.
  14. 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. 15. Practice Time!
  16. 16. 1) Find the missing angle.36°?°
  17. 17. 1) Find the missing angle.36°?°90 ° – 36 = 54°
  18. 18. 2) Find the missing angle.64°?°
  19. 19. 2) Find the missing angle.64°?°90 ° – 64° = 26°
  20. 20. 3) Solve for x.3x°2x°
  21. 21. 3) Solve for x.3x°2x°3x° + 2x° = 90°5x = 90x =18
  22. 22. 4) Solve for x.2x + 5x + 25
  23. 23. 4) Solve for x.2x + 5x + 25(2x + 5) + (x + 25) = 903x + 30 = 903x = 60x = 20
  24. 24. 5) Find the missing angle.?° 168°
  25. 25. 5) Find the missing angle.?° 168°180° – 168° = 12°
  26. 26. 6) Find the missing angle.58° ?°
  27. 27. 6) Find the missing angle.58° ?°180° – 58° = 122°
  28. 28. 7) Solve for x.4x 5x
  29. 29. 7) Solve for x.4x 5x4x + 5x = 1809x = 180x = 20
  30. 30. 8) Solve for x.2x + 10 3x + 20
  31. 31. 8) Solve for x.2x + 10 3x + 20(2x + 10) + (3x + 20) = 1805x + 30 = 1805x = 150x = 30
  32. 32. 9) Lines l and m are parallel.l||mFind the missing angles.42°lmb°d°f°a °c°e°g°
  33. 33. 9) Lines l and m are parallel.l||mFind the missing angles.42°lm42°42°42°138°138°138°138°
  34. 34. 10) Lines l and m are parallel.l||mFind the missing angles.81°lmb°d°f°a °c°e°g°
  35. 35. 10) Lines l and m are parallel.l||mFind the missing angles.81°lm81°81°81°99°99°99°99°
  36. 36. 11) Find the missing angles.70 °b°70 °d ° 65 °Hint: The 3 angles in atriangle sum to 180°.
  37. 37. 11) Find the missing angles.70 °40°70 °75 ° 65 °Hint: The 3 angles in atriangle sum to 180°.
  38. 38. 12) Find the missing angles.45 °b°50 °d ° 75 °Hint: The 3 angles in atriangle sum to 180°.
  39. 39. 12) Find the missing angles.45 °85°50 °20° 75 °Hint: The 3 angles in atriangle sum to 180°.
  40. 40. In the figure a || b.13. Name the angles congruent to ∠3.14. Name all the angles supplementary to ∠6.15. If m∠1 = 105° what is m∠3?16. If m∠5 = 120° what is m∠2?∠1, ∠5, ∠7∠1, ∠3, ∠5, ∠7105°60°
  41. 41. The End

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