Question 19
Circle TheoremsIn the diagram, PR is a targents to the circle at Q, QT//RS, ∠SQR = 35° and ∠RSQ = 50°. Find the value of ∠QST.
- A.40°
- B.65°
- C.85°
- D.95°
Show the answer and explanation
Answer: D (95°)
Explanation
In triangle QRS, ∠QRS = 95°. QT//RS gives ∠TQR = 180° − 95° = 85°, so ∠TQP = 95°. By the alternate segment theorem ∠QST = ∠TQP = 95°.