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← Figuring out angles between transversal and parallel lines

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Showing Revision 1 created 04/05/2014 by Report Bot.

  1. Let's say that we have
    two parallel lines.
  2. So that's one line
    right over there,
  3. and then this is
    the other line that
  4. is parallel to the first one.
  5. I'll draw it as
    parallel as I can.
  6. So these two lines are parallel.
  7. This is the symbol
    right over here
  8. to show that these two
    lines are parallel.
  9. And then let me draw
    a transversal here.
  10. So let me draw a transversal.
  11. This is also a line.
  12. Now, let's say that we know
    that this angle right over here
  13. is 110 degrees.
  14. What other angles can
    we figure out here?
  15. Well, the first thing
    that we might realize
  16. is that, look, corresponding
    angles are equivalent.
  17. This angle, the angle
    between this parallel line
  18. and the transversal,
    is going to be
  19. the same as the angle
    between this parallel line
  20. and the transversal.
  21. So this right over here is
    also going to be 110 degrees.
  22. Now, we also know that
    vertical angles are equivalent.
  23. So if this is 110
    degrees, then this angle
  24. right over here on the opposite
    side of the intersection
  25. is also going to be 110 degrees.
  26. And we could use that
    same logic right over here
  27. to say that if this
    is 110 degrees,
  28. then this is also 110 degrees.
  29. We could've also
    said that, look,
  30. this angle right over here
    corresponds to this angle
  31. right over here so that they
    also will have to be the same.
  32. Now, what about
    these other angles?
  33. So this angle right over
    here, its outside ray,
  34. I guess you could
    say, forms a line
  35. with this angle right over here.
  36. This pink angle is supplementary
    to this 110 degree angle.
  37. So this pink angle plus 110
    is going to be equal to 180.
  38. Or we know that this pink angle
    is going to be 70 degrees.
  39. And then we know that it's a
    vertical angle with this angle
  40. right over here, so
    this is also 70 degrees.
  41. This angle that's kind of
    right below this parallel line
  42. with the transversal, the bottom
    left, I guess you could say,
  43. corresponds to this bottom
    left angle right over here.
  44. So this is also 70 degrees.
  45. And we could've also
    figured that out by saying,
  46. hey, this angle is supplementary
    to this angle right over here.
  47. And then we could use
    multiple arguments.
  48. The vertical angle argument,
    the supplementary argument two
  49. ways, or the corresponding
    angle argument to say that,
  50. hey, this must be
    70 degrees as well.