Praise be to Allah.
The talaaq in which the husband is allowed to take back his wife is the first or second talaaq. If he divorces her a third time, she becomes a stranger to him (non-mahram) and she is not permissible for him until she has married another husband and the marriage has been consummated. Allaah says (interpretation of the meaning):
“The divorce is twice, after that, either you retain her on reasonable terms or release her with kindness. And it is not lawful for you (men) to take back (from your wives) any of your Mahr (bridal-money given by the husband to his wife at the time of marriage) which you have given them, except when both parties fear that they would be unable to keep the limits ordained by Allaah (e.g. to deal with each other on a fair basis). Then if you fear that they would not be able to keep the limits ordained by Allaah, then there is no sin on either of them if she gives back (the Mahr or a part of it) for her Al-Khul‘ (divorce). These are the limits ordained by Allaah, so do not transgress them. And whoever transgresses the limits ordained by Allaah, then such are the Zaalimoon (wrongdoers).
230. And if he has divorced her (the third time), then she is not lawful unto him thereafter until she has married another husband. Then, if the other husband divorces her, it is no sin on both of them that they reunite, provided they feel that they can keep the limits ordained by Allaah. These are the limits of Allaah, which He makes plain for the people who have knowledge”
It is not a condition of divorce that the woman should hear it from her husband or know of it. If a man issues the divorce verbally or in writing, whether in her presence or in her absence, then the divorce takes effect.
With regard to anger, it depends on the situation.
If it is mild anger and does not affect his will or choice, then the divorce takes effect and is valid.
If the anger is so intense that he does not know or realize what he is saying, then this divorce does not count, because he is like one who is insane, who is not to be taken to task for what he says.
In these two cases, there is no dispute among the scholars. There remains a third type of anger, which is intense anger that affects a man’s will, so he speaks and it is as if he is pushed to say what he says, but he quickly regrets it as soon as his anger dissipates, but he did not reach a point where he did not know what he was saying or doing. There is a difference of scholarly opinion with regard to this kind of anger. We have discussed that in the answer to question no. 22034.
And Allaah knows best.