PQ and RS are two chords in a circle with centre O and PS is a diameter. PQ and RS produced to meet at a point T outside the circle. If ∠PTR = 25° and ∠SPT = 39°, then the measure of ∠SQR is?
Answer & explanation
Correct answer: option 2
∠SQP = 90° (angle made by diameter is always 90°)
angel made by chord on circumference are same so ∠P = ∠R = 39°
∠PSR = ∠SPT + ∠STP (exterior angle)
= 39° + 25° = 64°
∠PSQ = 90° - 39° = 51°
In ΔQRS
∠QSR + ∠SRQ + ∠RQS = 180°
∠RQS + 39° + 64° + 51° = 180°
∠RQS = 26° = ∠SQR