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Geometry

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The three angles of a triangle have measures 12x degree, 3x degree, and 7y degree, where 7y>60. If x and y are integers, what is the value of x?

  • Geometry - ,

    12x + 3x + 7y = 180
    15x + 7y = 180
    15x + 60 < 180
    15x < 120
    x < 8

    check:
    pick a value of x,
    1. x < 8 , e.g. let x = 4
    then 48+12 + 7y = 180
    7y = 120 , so 7y > 60 , OK!

    2. x > 8 , e.g. x = 10
    then 150 + 30 + 7y = 180
    7y = 0 , and 7y > 60 is false

    Therefore x < 8 is correct.

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