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Math Help - value of x in an isosceles triangle

  1. #1
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    value of x in an isosceles triangle

    hi,this is my question:

    triangle ABC is isosceles.
    one angle is x.
    another angle is 4x.

    find the two possible values of x.

    im unsure how to work this out, i know that in an isosceles triangle 2 angles are equal.

    could someone tell me how to work this question out please?

    thanks!
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  2. #2
    Super Member TheChaz's Avatar
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    Let's say we have angles A, B, and C.
    You know that two of them are x and 4x.
    So let's say that A is the one that is x, and B is the one that is 4x. It doesn't matter which we choose (mathematicians use the phrase "without loss of generality" before making such assumptions, FYI).

    So we have A + B + C = 180. What is C? Well, since it's an isosceles triangle, C must equal one of the other two. C must equal x OR C must equal 4x.
    Start with the first case: C = x
    Then A + B + C = 180 becomes
    x + 4x + x = 180. Solve for x.

    Second case: C = 4x
    Then A + B + C = 180 becomes
    x + 4x + 4x = 180. Solve for x.

    Those are your two values for x!
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