Question 31
Circle TheoremsMN is a tangent to the given circle at M, MR and MQ are two chords. If QM̂N is 60° and MN̂Q is 40°, find RM̂Q
- A.120°
- B.110°
- C.60°
- D.20°.
Show the answer and explanation
Answer: D (20°.)
Explanation
By the alternate segment theorem angle MRQ = angle QMN = 60°. In triangle MQN, angle MQN = 180° − 60° − 40° = 80°, so angle MQR = 100°. In triangle MRQ, angle RMQ = 180° − 60° − 100° = 20°.