
zusagen
to accept
To accept an invitation or an offer; to confirm one's participation or agreement.
Ich habe für die Party am Samstag zugesagt.
I accepted the invitation for the party on Saturday.
to accept / promise / appeal
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to accept
To accept an invitation or an offer; to confirm one's participation or agreement.
Ich habe für die Party am Samstag zugesagt.
I accepted the invitation for the party on Saturday.

to promise
To firmly promise or guarantee something to someone.
Der Handwerker hat zugesagt, die Reparatur bis morgen abzuschließen.
The handyman promised to finish the repair by tomorrow.

to appeal to someone
To please someone or be appealing to someone; to match someone's taste or ideas.
Das Jobangebot in Hamburg sagt mir nicht wirklich zu.
The job offer in Hamburg doesn't really appeal to me.
'Zusagen' is a separable verb. The prefix 'zu' comes at the end in a main clause; in subordinate clauses the verb stays together, and in the infinitive with 'zu', the form 'zuzusagen' is formed.
Er sagte sofort für das Projekt zu.
He immediately agreed to take part in the project.
The verb is made up of the prefix 'zu' and the verb 'sagen' (to say). The prefix 'zu' signals agreement or positive confirmation here, literally 'Ja sagen' (to say yes).
Können Sie mir bis morgen zusagen?
Can you confirm by tomorrow?
In the meaning 'gefallen' (to please / to appeal), 'zusagen' is always used with a dative object. The subject is the thing that is pleasing, and the person it appeals to is in the dative.
Die neue Wohnung sagt uns sehr zu.
The new apartment really appeals to us.
When you accept an invitation, 'zusagen' is often used directly or with the preposition 'für' (for). Typical combinations are 'eine Einladung zusagen' (to accept an invitation), 'seine Teilnahme zusagen' (to confirm one's participation), or 'für eine Feier zusagen' (to accept an invitation to a celebration).
Wir haben für die Hochzeit unserer Freunde zugesagt.
We accepted the invitation to our friends' wedding.
When 'zusagen' means 'versprechen' (to promise), it is often followed by a subordinate clause with 'dass' (that) or an infinitive construction with 'zu' (to) to describe the promise.
Der Chef sagte zu, dass wir mehr Unterstützung bekommen.
The boss promised that we would get more support.
to lie / be located
A task liegt jemandem when it matches the person’s abilities or inclinations. It sagt jemandem zu when the person views it positively and likes it according to their personal preferences. For natural aptitude, liegen is the better choice; for enjoyment or satisfaction, zusagen is more precise.

Die Arbeit mit Kindern sagt Mia zu, weil ihr das freundliche Team gefällt.
Working with children appeals to Mia because she likes the friendly team.
Die Arbeit mit Kindern liegt Mia, weil sie geduldig und aufmerksam ist.
Working with children suits Mia because she is patient and attentive.