The cliche “I am glad you asked me that” enables you to gain thinking time and you should develop a few more original phrases to help you organize your thoughts before and even during your answer. Here are some suggestions:
• “To help me answer your question more accurately, could you tell me exacdy why you are asking it?”
• “I can see that you feel strongly about that and I admire you for saying so.”
Sometimes you will not want to answer a question, so you should think of how you can deflect it:
• “We have spent some time on that problem/question, but what I think is more relevant to consider now is.. . . ”
• “There is some merit in those points and it has been useful to hear from you but perhaps you are not aware that....”