What is the difference between "sich ärgern über", "wütend sein auf", and "genervt sein von", when all of them mean "be angry about"? Could you please give some examples?

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"Be angry about" is only a very, very rough translation of these three German terms. The English language has its own ways to express the subtleties. A good dictionary should give you valuable assistance.

Here are sample sentences showing the typical use of sich ärgern über, wütend sein auf, genervt sein von.

Sich ärgern über is a (default, standard, moderate) form of being angry

Paul ärgert sich über seine schlechte Note in Deutsch.

Beate ärgert sich über ihren Bruder, weil er vergessen hat, sie vom Bahnhof abzuholen.

Wütend sein auf/über is being in a rage, i.e. very angry:

Paul ist wütend auf Barbara, weil sie seinen Hamster mit dem Dreirad totgefahren hat.

Beate ist wütend, weil Fritz sie mit Ines betrogen hat.

Genervt sein von is a form of being annoyed (or slightly angry)

Karl ist genervt von seinem Handy, das immer so laut piepst, wenn der Strom alle ist.

Marie ist genervt von ihrem Bruder, weil er seine Socken immer überall rumliegen lässt.

Note on registers of style:

Sich ärgern and wütend sein are pretty much default (neutral) mode of language. Genervt sein, however, is rather from the private and casual sectors of life; you would rather not use this word in official communication. Instead you may used irritiert sein über (which is very formal). - But also if you use irritiert sein über in a context where genervt sein von is expected, e.g. in your group of 16 year old peers, they would be pretty irritated and complain: "Du nervst!"

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