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pratu043

In the given figure, AB divides DAC in the ratio 1:3 and AB = DB. Calculate the unknown angles.

  • one year ago
  • one year ago

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  1. pratu043
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    |dw:1342757653054:dw|

    • one year ago
  2. pratu043
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    @lgbasallote please help!!

    • one year ago
  3. lgbasallote
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    |dw:1342757791245:dw| just presenting a drawing first so i can visualize it

    • one year ago
  4. pratu043
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    I figured out that angle ADB = y.

    • one year ago
  5. lgbasallote
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    how did you figure that out?

    • one year ago
  6. lgbasallote
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    oh i see

    • one year ago
  7. pratu043
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    Because triangle ABD is isosceles.

    • one year ago
  8. lgbasallote
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    |dw:1342757924763:dw|

    • one year ago
  9. pratu043
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    And how did you get DB = 3a and BC = a?

    • one year ago
  10. lgbasallote
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    it says the ratio is 1:3

    • one year ago
  11. pratu043
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    Ratio is 1:3 for the angle DAC.

    • one year ago
  12. pratu043
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    That means t = 3a and y = a.

    • one year ago
  13. lgbasallote
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    oh lol

    • one year ago
  14. lgbasallote
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    y + y + t + 90 = 180 2y + t = 90 do you see this?

    • one year ago
  15. pratu043
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    How did you get x = 90 degrees? I know it looks like that but i doesn't say so in the question.

    • one year ago
  16. pratu043
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    Yes, I got that.

    • one year ago
  17. lgbasallote
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    according to your triangle it's a right triangle

    • one year ago
  18. pratu043
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    I might be slightly greater or lesser that 90 right?

    • one year ago
  19. lgbasallote
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    |dw:1342758203033:dw| y + y + m = 180 t + 90 + n = 180 m + n = 180

    • one year ago
  20. pratu043
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    *It.

    • one year ago
  21. lgbasallote
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    what do you mean?

    • one year ago
  22. lgbasallote
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    do you have the *real* drawing??

    • one year ago
  23. lgbasallote
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    this drawing is getting confusing :(

    • one year ago
  24. pratu043
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    Yes, but it is in the form of a worksheet that I got in school(it is not in the electronic form).

    • one year ago
  25. pratu043
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    I'll try drawing again then, just a minute.

    • one year ago
  26. pratu043
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    |dw:1342758349890:dw|

    • one year ago
  27. pratu043
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    |dw:1342758495805:dw| For convenience.

    • one year ago
  28. pratu043
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    The question given along with the drawing is the original one at the top and as you can see, there's nothing saying x is a right angle.

    • one year ago
  29. lgbasallote
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    |dw:1342758686754:dw| a + a + x = 180 n + 3a + x = 180 a + a + m = 180 m + n = 180 do you see these?

    • one year ago
  30. pratu043
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    Yes I do.

    • one year ago
  31. lgbasallote
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    so you have 4 unknowns and 4 equations. we can use systems of linear equations

    • one year ago
  32. pratu043
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    Yeah, but I only know how to solve system of equations with 2 variables.

    • one year ago
  33. lgbasallote
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    i wrote one wrong...should be a + (a+3a) + x = 180

    • one year ago
  34. pratu043
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    So 5a + x = 180

    • one year ago
  35. lgbasallote
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    a + a + 3a + x = 180 -->1 n + 3a + x = 180 ---> 2 a + a + m = 180 --->3 m + n = 180 --> 4 yes

    • one year ago
  36. lgbasallote
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    let's simplify everything first 5a +x = 180 n + 3a + x = 180 2a + m = 180 m + n = 180

    • one year ago
  37. pratu043
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    OK. What next?

    • one year ago
  38. lgbasallote
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    now we subtract equation 2 from equation 1 5a + x = 180 - 3a + x + n = 180 =========== 2a + 0 + n = 0 =========== 2a + n = 0 =========== 2a = -n

    • one year ago
  39. lgbasallote
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    ^that would be equation 5

    • one year ago
  40. pratu043
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    Shouldn't it be 2a = n? Because 0 - n would be -n and but you wrote n.

    • one year ago
  41. lgbasallote
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    uhmm yeah you're right 2a = n

    • one year ago
  42. pratu043
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    So a = n/2. Or we can use n = 2a in one of the equations?

    • one year ago
  43. lgbasallote
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    2a = n is the 5th equation

    • one year ago
  44. pratu043
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    5a +x = 180 n + 3a + x = 180 2a + m = 180 m + n = 180 2a = n

    • one year ago
  45. lgbasallote
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    now look at m + n = 180 i can also say n = 180 - m <--i'll substitute this into the 2nd equation n + 3a + x = 180 180 -m + 3a + x = 180 3a - m + x = 0 <--6th equation

    • one year ago
  46. pratu043
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    Are you sure this is 9th standard level? Because our math teacher hasn't taught us this yet. We have only reached linear equations in two variables.

    • one year ago
  47. lgbasallote
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    well...x is not 90 degrees....

    • one year ago
  48. lgbasallote
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    it's seriously complicated

    • one year ago
  49. pratu043
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    |dw:1342759662640:dw|

    • one year ago
  50. lgbasallote
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    if x were 90 then i assume the right triangle postulates and theorems could be applied

    • one year ago
  51. lgbasallote
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    or maybe im just doing something wrong here...

    • one year ago
  52. lgbasallote
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    @dpaInc

    • one year ago
  53. pratu043
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    Angle ABC = 180 - (3a + x).

    • one year ago
  54. pratu043
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    a + 4a + x = 180 or 5a + x = 180

    • one year ago
  55. pratu043
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    This is still not getting us anywhere ....

    • one year ago
  56. pratu043
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    |dw:1342759792383:dw|

    • one year ago
  57. pratu043
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    Is it possible to get x in terms of a ?

    • one year ago
  58. lgbasallote
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    @dpaInc help here

    • one year ago
  59. pratu043
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    |dw:1342760301927:dw| If we take XY parallel to AB then AC is a transversal.

    • one year ago
  60. pratu043
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    @dpaInc you should find a, 3a and x.(in the latest figure)

    • one year ago
  61. pratu043
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    Are you there @dpaInc?

    • one year ago
  62. dpaInc
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    yep... just trying to figure it out....:)

    • one year ago
  63. dpaInc
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    |dw:1342761130552:dw|

    • one year ago
  64. dpaInc
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    i don't think the there is a unique solution.... are you looking for integer solutions?

    • one year ago
  65. pratu043
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    I have to go now. Please please please help if possible .....

    • one year ago
  66. mukushla
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    i think dplanc is right there is no unique solution unless x=90

    • one year ago
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