
ansagen
to announce
To announce something publicly, for example the next song, the next program item, or the next stop.
Der Schaffner sagte den nächsten Halt an.
The conductor announced the next stop.
to announce
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to announce
To announce something publicly, for example the next song, the next program item, or the next stop.
Der Schaffner sagte den nächsten Halt an.
The conductor announced the next stop.

to declare war on
A fixed expression that means deciding to take active action against a person, thing, or situation.
Die Regierung hat der Korruption den Kampf angesagt.
The government has declared war on corruption.

to announce
Colloquial for proclaiming a clear intention or taking the lead and deciding what will be done.
Der Trainer hat für die nächste Saison den Aufstieg angesagt.
The coach has announced promotion for next season.

to declare
In card games, to declare a particular type of game or the trump suit.
Beim Skat muss man vor dem ersten Stich ansagen, welches Spiel man spielt.
In Skat, you have to declare which game you are playing before the first trick.
'Ansagen' is a separable verb. The prefix 'an-' goes at the end in a main clause. In subordinate clauses or after a modal verb, the verb stays together.
Der Moderator sagt den nächsten Gast an.
The host announces the next guest.
You can often recognize which meaning is intended from the object. If you say 'einen Halt' (a stop) or 'ein Lied' (a song) with 'ansagen', it is an announcement. If you say 'den Kampf' (the fight), it is a declaration of war. If you say 'den Sieg' (victory), it is a confident claim.
Im Zug wurde der nächste Bahnhof angesagt.
The next station was announced on the train.
In the meaning 'ankündigen' (to announce), 'ansagen' is often used for public information. Typical phrases are: 'eine Haltestelle ansagen' (to announce a stop), 'das Wetter ansagen' (to announce the weather), 'einen Programmpunkt ansagen' (to announce a program item), or 'ein Lied ansagen' (to announce a song).
Im Radio wurde gerade ein Stau auf der A5 angesagt.
A traffic jam on the A5 was just announced on the radio.
The expression 'jemandem/etwas den Kampf ansagen' (to declare war on someone/something) is fixed. The person or thing you want to fight against is always in the dative.
Die Ärztin hat den Kilos den Kampf angesagt und eine Diät begonnen.
The doctor declared war on the kilos and started a diet.
When 'ansagen' announces an intention or goal, the usage is colloquial. It often expresses great self-confidence or a challenge.
Vor dem Spiel hat der Kapitän den Sieg angesagt.
Before the game, the captain announced victory.
to announce
Both verbs can be used to announce an upcoming event publicly. Ankündigen is more general and can also happen in writing or in advance; ansagen typically refers to a specific public announcement, for example as part of a program or at a stop. Choose ansagen when something is presented directly and orally.

Die Moderatorin sagte den nächsten Programmpunkt direkt auf der Bühne an.
The presenter announced the next item on the program directly from the stage.
Das Theater kündigte den neuen Spielplan schon im Internet an.
The theater announced the new season's program online well in advance.