In the given figure, ∠TQR = 49° and QT is the diameter of the circle. What is the value of ∠QTR + ∠QSR + ∠QPR?
Show answer & explanation
Correct answer: D
Explanation
Given:
∠TQR = 49° and QT is the diameter of the circle.
In triangle QRT:
∠QRT = 90°
∠QTR = 180° − (90° + 49°) = 41°
∠QTR, ∠QSR, and ∠QPR are all angles subtended at the circumference by the same chord, QR.
∠QTR = ∠QSR = ∠QPR = 41°
∠QTR + ∠QSR + ∠QPR
= 41° + 41° + 41°
= 123°