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 ?
Answer & explanation
Correct answer: option 1
∠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°.