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Answer :
Final answer:
The question is asking you to apply geometric properties of line segments to find a certain length. After solving for x, you can use the given equations and values to find that SQ equals 77.
Explanation:
This question is about geometry, specifically the properties of line segments. If SR bisects PT, then the two segments it forms, PQ and QT, are equal in length. This translates to the equation 12x + 7 = 8x + 27.
Solving this equation for x gives us x = 4.
Now, we can find the length of SQ, which is the sum of SR and QR.
Substituting the given values into the equation SR = 6x + 30 gives us SR = 54, and QR is given as 23, so
SQ = SR + QR
= 54 + 23
= 77.
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