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Math Help - parallel line angles

  1. #1
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    parallel line angles

    In the figure above, four lines intersect as shown. If a = 30 and line is parallel to line m, how many of the seven angles marked with arrows must have measure 30?

    1. One
    2. Three
    3. Four
    4. Five
    5. Seven

    I think the correct answer is 7, am i correct?
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  2. #2
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    Incorrect.

    Look carefully at your diagram. The horizontal lines (l) and (m) are given as parallel. The diagonal lines are not proven to be parallel, thus:

    We know that only 3 of the 7 angles marked are definitely 30 degrees.

    Read the question carefully

    //j0k3r
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  3. #3
    MHF Contributor kalagota's Avatar
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    yes, joker is correct.
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  4. #4
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    Quote Originally Posted by j0k3r View Post
    Incorrect.

    Look carefully at your diagram. The horizontal lines (l) and (m) are given as parallel. The diagonal lines are not proven to be parallel, thus:

    We know that only 3 of the 7 angles marked are definitely 30 degrees.

    Read the question carefully

    //j0k3r
    Which three? I know that a and the angle directly facing angle a are 30 degree. Which other angle is 30 degrees? And why?

    Thanks in advance

    And thanks to j0k3r for replying!!
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  5. #5
    MHF Contributor kalagota's Avatar
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    use, alternate interior angle theorem to the determine the other one and the vertical angle theorem after for the last one..
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  6. #6
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    a and b must be the same as they are opposite one another.


    because l and m are parallel, a and c must also be exactly the same. and due to the opposite rule, d and c are the same.

    //j0k3r
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