Intense Angle Chasing!

Geometry Level 3

Point \(H\) is the orthocenter of triangle \(ABC\). Points \(D, E, \) and \(F\) lie on the circumcircle of triangle \(ABC\) such that \(AD || BE || CF \). Points \(S, T, \) and \(U\) are the respective reflections of \(D, E, \) and \(F\) across the lines \(BC, CA, \) and \(AB\). Given that two angles of quadrilateral \(SHUT\) (may not be in this orientation) are \(39\) degrees and \(91\) degrees. Find the positive difference between the other two angles.

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