geometry

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The line QS bisects <PQR, m<PQR = (x2), and m<PQS = (2x +6). Find all the possible measures for <PQR.

  • geometry -

    PQR = X^2.
    PQS = 2x + 6.

    PQS = PQR/2,
    2x + 6 = X^2/2,
    Multiply both sides by 2:
    4x + 12 = X^2,
    x^2 - 4x - 12 = 0,
    (x+2)(x-6) = 0,

    x+2 = 0,
    X = -2.

    x-6 = 0,
    X = 6.

    PQR = X^2 = (-2)^2 = 4.
    PQR = 6^2 = 36.

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