# 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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