O is the center of a circle, and PQ and RS are two chords. When PQ and RS are extended, they meet at point K. If PR is a diameter and ∠PKS = 66°, what is the value of ∠QOS?
Show answer & explanation
Correct answer: B
Explanation
Given:
PR is the diameter, ∠PKS = 66°
According to the formula:
Exterior angle = 180° − (Central angle / 2)
66 = 180 − (∠QOS / 2)
∠QOS / 2 = 114
∠QOS = 228°
Minor central angle = 360° − 228° = 132°
Now, corresponding to the arc:
∠QOS = 2 × (66 − 42) = 48°