The better question is if it's appropriate for the therapist to answer personal questions asked by the client. As a client you can ask anything you want, but the therapist doesn't have to answer your questions if they are personal.

Whether it's advisable, appropriate or ethical for the therapist to answer personal questions depends on whether the therapist believes that his or her answer would be therapeutically beneficial for the client.

If the therapist feels that answering the question would benefit the client, he or she should use self-disclosure wisely and sparingly. Excessive self-disclosure may become an ethical issue because it can indicate that the therapist is trying to fulfill his or her own emotional needs rather than attend to the needs of the client'