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Math Help - angle size

  1. #1
    Member Veronica1999's Avatar
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    angle size

    Mark the point P inside a square ABCD that makes the triangle CDP equilateral. Calculate the size of angle PAD?

    I got around 77. (I used a protractor)
    Could I get some hints on how to get the angle?
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  2. #2
    Junior Member
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    First you should have a clear idea of what the thing you've drawn looks like:
    angle size-namnloes.gif

    I've taken the liberty to highlight the angles I find important for solving this problem.

    Then you should take note that all angles within triangle DCP are the same, and that they add up to 180 degrees.

    Also you should notice that \angle{APD}=\angle{PAD}~\mbox{since}~\triangle{APD  }~\mbox{is isosceles}

    And lastly, you should notice that \angle{ADP}+\angle{PDC}=\angle{ADC}=90^\circ

    One last point: never use a protractor(or any other tool for that matter) to solve a geometrical problem of any kind, unless the problem explicitly states that you should. The risk that you will end up with a faulty answer(which you actually did in this case) is huge.
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  3. #3
    Super Member
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    Hi Veronica 1999,
    A short answer
    Drop a perpendicular to DC from P . Knowing the properties of a 30-60-90 triangle what can you say about DA andDP ?



    bjh
    Last edited by bjhopper; March 6th 2011 at 12:39 PM. Reason: left out words
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  4. #4
    Senior Member abhishekkgp's Avatar
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    Triangle PAD is isoceles with angle-PDA being 30 deg.
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