wütend
angry
To feel very strong anger or irritation.
Sie war wütend auf ihn, weil er sie angelogen hatte.
She was angry at him because he had lied to her.

angry
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angry
To feel very strong anger or irritation.
Sie war wütend auf ihn, weil er sie angelogen hatte.
She was angry at him because he had lied to her.

The adjective 'wütend' (angry) belongs to the word family around the noun 'die Wut' (anger/rage). 'Die Wut' is the feeling of strong anger itself.
Seine Wut war so groß, dass er den Raum verließ.
His anger was so great that he left the room.
The preposition depends on the reason for the anger. You are 'wütend auf' (angry at) a person (accusative) or 'wütend über' (angry about) a thing or situation (accusative).
Ich bin wütend auf meinen Bruder, weil er zu spät gekommen ist.
I am angry at my brother because he came too late.
Common constructions are 'wütend werden' (to become angry), to describe the beginning of the feeling, and 'jemanden wütend machen' (to make someone angry), to express the cause.
Sei bitte leise, sonst wird Papa wütend.
Please be quiet, otherwise Dad will get angry.
quiet / calm
'ruhig' and 'wütend' can both describe a person's inner state. In this sense, 'ruhig' means that someone is composed and does not get upset. 'wütend' means that someone feels very strong anger. Here they are clear opposites: a calm person stays in control, while an angry person is highly emotionally upset. So when it comes to feelings, 'ruhig' is the opposite of 'wütend'.

Emma war wütend, weil der Schiedsrichter das Tor nicht gezählt hatte.
Emma was angry because the referee had not counted the goal.
Vor der Prüfung bleibt Lena ruhig und atmet tief durch.
Before the exam, Lena stays calm and takes a deep breath.