In a circle, O is the center of the circle. Chords PQ and RS intersect at T. If ∠POS = 32° and ∠ROQ = 26°, then the measure of ∠PTS lies between ?

25° and 30°

∠QST = \(\frac{1}{2}\) ∠ROQ

∠QST = \(\frac{1}{2}\) (26°) = 13°

∠SQT = \(\frac{1}{2}\) ∠POS = \(\frac{1}{2}\) (32°) = 16°

∠PTS is the exterior angle of ΔSTQ

∴ ∠PTS = ∠TSQ + TQS

         = 13° + 16° = 29°

So, ∠PTS lies between 25° and 30°.