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Math Help - Finding one angle of a right triangle with given information

  1. #1
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    Finding one angle of a right triangle with given information

    Finding one angle of a right triangle with given information-gmat-triangle.jpg

    I am currently studying for the GMAT which tests on Data Sufficiency. According to the test, I should be able to answer this question with the given statement, but I can't figure out how.

    In the figure shown, the measure of angle PRS is how much greater than the measure of angle PQR?

    How can I find that answer if the only information I have is this?

    "The measure of angle QPR is 30 degrees."
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  2. #2
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    Re: Finding one angle of a right triangle with given information

    Quote Originally Posted by KingNathan View Post
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    I am currently studying for the GMAT which tests on Data Sufficiency. According to the test, I should be able to answer this question with the given statement, but I can't figure out how.
    In the figure shown, the measure of angle PRS is how much greater than the measure of angle PQR?

    How can I find that answer if the only information I have is this?

    "The measure of angle QPR is 30 degrees."
    Angle PRS is the external angle of triangle PQR.
    Angle PRS is the sum of which 2 angles in triangle PQR ?
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  3. #3
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    Re: Finding one angle of a right triangle with given information

    Quote Originally Posted by Archie Meade View Post
    Angle PRS is the external angle of triangle PQR.
    Angle PRS is the sum of which 2 angles in triangle PQR ?
    I am struggling to find the values for angles PRQ and PQR. I am assuming that I am forgetting a rule about triangles. These are the assumptions I can draw from the information given.

    Angle QPR is 30 degrees
    Angle PSR is 90 degrees
    Angle QPS must be larger than 30 degrees
    Angle PRQ is 180 degrees-Angle PRQ

    However, I can't seem to derive a value from the information given that gives me the value for neither Angle PQE nor Angle PRQ
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  4. #4
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    Re: Finding one angle of a right triangle with given information

    You could work from..

    Angle PRS + Angle PRQ is 180 degrees (a semicircle).
    The sum of all 3 angles in triangle PQR is also 180 degrees.

    One of these is Angle PRQ.

    This means that Angle PRS is the sum of the other 2 angles in triangle PQR.
    The question can then be answered.

    The strategy here is "angles summing to 180 degrees"
    and Angle PRS is common to both sums.
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  5. #5
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    Re: Finding one angle of a right triangle with given information

    Quote Originally Posted by Archie Meade View Post
    You could work from..

    Angle PRS + Angle PRQ is 180 degrees (a semicircle).
    The sum of all 3 angles in triangle PQR is also 180 degrees.

    One of these is Angle PRQ.

    This means that Angle PRS is the sum of the other 2 angles in triangle PQR.
    The question can then be answered.

    The strategy here is "angles summing to 180 degrees"
    and Angle PRS is common to both sums.
    I apologize, and do greatly appreciate the time you are taking to help me. However, I still do not understand. I see we have only 1 angle value for each of the 2 triangles. I can't see how Angle QPR equalling 30 degrees shows us the value of any other angle in either triangle.
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  6. #6
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    Re: Finding one angle of a right triangle with given information

    For convenience, label Angle PRS "A",
    label Angle PRQ "B".

    Then A+B = 180 degrees.

    Label Angle PQR "C".

    Then B+C+30 degrees = 180 degrees.

    Then A=180-B
    C=180-(B+30)=180-B-30

    So "A" is 30 degrees bigger than "C".
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  7. #7
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    Re: Finding one angle of a right triangle with given information

    Quote Originally Posted by Archie Meade View Post
    For convenience, label Angle PRS "A",
    label Angle PRQ "B".

    Then A+B = 180 degrees.

    Label Angle PQR "C".

    Then B+C+30 degrees = 180 degrees.

    Then A=180-B
    C=180-(B+30)=180-B-30

    So "A" is 30 degrees bigger than "C".
    Awesome! Thanks for your help.
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