Problem D

Many Ways to Get There

Rectangle \(PQRS\) has \(QR=4\) and \(RS=7\). \(\triangle TRU\) is inscribed in rectangle \(PQRS\) with \(T\) on \(PQ\) such that \(PT=4\), and \(U\) on \(PS\) such that \(SU=1\).

Determine the value of \(\angle RUS+\angle PUT\).

There are many ways to solve this problem. After you have solved it, see if you can solve it a different way.