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__Intersecting chords or secants theorem:__

m∠PTR = 1/2 (arc PR + arc QS)

m∠PTR =

__45° + 49°__

2

m∠PTR = 94°/2

m∠PTR = 47°

∠PTR and ∠RTS are supplementary angles:

∠PTR + ∠RTS = 180°

180° - 47° = ∠RTS

∠RTS = 133°

From Vertical Angles Theorem where non-adjacent angles formed by two intersecting lines are congruent, we can conclude that the other angles' measurements are:

∠PTR = ∠QTS

∠QTS = 47°

∠RTS = ∠PTQ

∠PTQ = 133°