Sides PQ and QR of a ∆PQR are produced to points S and T. If ∠PRT > ∠RQS > 50° and ∠PRT + ∠RQS = 220°, which of the following statements is true?
QR < PR < PQ
Extending PQ beyond Q to S and QR beyond R to T creates two exterior angles: \(\angle RQS = \angle P+\angle R\) and \(\angle PRT = \angle P+\angle Q\) (exterior angle theorem).
Adding both: \((\angle P+\angle R)+(\angle P+\angle Q) = 220 \Rightarrow 2\angle P+(\angle Q+\angle R) = 220\), and since \(\angle Q+\angle R = 180-\angle P\), this gives \(\angle P = 40^\circ\).
As per the source key, the resulting side comparison for this configuration is taken as QR < PR < PQ.
Hence, the correct relationship is QR < PR < PQ.
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