verärgern
to annoy / upset
To make someone annoyed or angry; to cause someone displeasure or anger.
Seine ständige Unpünktlichkeit verärgert die Kollegen sehr.
His constant unpunctuality really annoys his colleagues.

to annoy / upset
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to annoy / upset
To make someone annoyed or angry; to cause someone displeasure or anger.
Seine ständige Unpünktlichkeit verärgert die Kollegen sehr.
His constant unpunctuality really annoys his colleagues.

The verb 'verärgern' (to annoy/upset) is derived from the noun 'der Ärger' (annoyance/anger). The prefix 'ver-' is used here to form a verb meaning to put someone into a state of annoyance or anger.
Sein respektloses Verhalten hat mich wirklich verärgert.
His disrespectful behavior really upset me.
The person or thing that causes the annoyance is the subject of the sentence. The person who becomes annoyed is the accusative object.
Die laute Musik aus der Nachbarwohnung verärgert mich.
The loud music from the neighboring apartment annoys me.
The past participle 'verärgert' (annoyed/upset) is very often used like an adjective to describe a person's state. It is often used together with the preposition 'über' (+ accusative).
Er war sichtlich verärgert über die Verspätung des Busses.
He was visibly annoyed about the bus being late.
to upset / excite
'aufregen' and 'verärgern' can both have to do with anger. More specifically, 'verärgern' means that someone is made annoyed or angry. 'aufregen' is broader: you can get angry about something, but also become nervous or worried. For this reason, learners may confuse the words when the topic is anger. If only anger is meant, 'verärgern' fits very precisely. If the reaction is generally emotional, nervous, or strong, 'aufregen' is more natural.

Aylin verärgert ihren Kollegen, weil sie den Termin ohne Absprache verschiebt.
Aylin annoys her colleague because she reschedules the appointment without discussing it first.
Nach der Arbeit will ich mich nicht mehr über das Gespräch aufregen.
After work, I don't want to get upset about the conversation anymore.