Does a divorce issued by a husband in a state of anger take effect, after his wife claimed that she touched a strange man and took his number with the intent to spite him?

The default ruling is that anger does not prevent a divorce from occurring, unless the anger reaches a point where awareness is lost. So long as the man is aware of what he is saying, the divorce takes place. If it was the first or second divorce, he may reconcile with his wife as long as she is still within her iddah (definition) (waiting period). If it was the third divorce, then his wife is unlawful for him, and it is an irrevocable divorce (baynunah kubra). She will not become lawful for him until she marries another man in a valid marriage and is subsequently divorced. The questioner is advised to go to the Sharia (definition) court to resolve the matter and to avoid anger, as stated in the Prophet's (peace be upon him) advice: "Do not get angry." It is also advisable to avoid places where men and women mix excessively.