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°
