Question 23
Circle TheoremsTwo chords PQ and RS of a circle when produced meet at K. If ∠KPS = 31° and ∠PKR = 42°, find ∠KQR
- A.11°
- B.73°
- C.107°
- D.138°
- E.149°
Show the answer and explanation
Answer: C (107°)
Explanation
In triangle KPS, ∠KSP = 180° − 31° − 42° = 107°. In cyclic quadrilateral PQRS, the exterior angle ∠KQR equals the interior opposite angle ∠PSR, so ∠KQR = 107°.