So... is Ange Vierge finished or not?
NO, it is not finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Five interconnected worlds, each with distinct characteristics, are suddenly thrown into chaos when a mysterious event called the World Connect threatens their very existence.
An alien species, Ouroboros, seeks to exploit this chaos and hasten the universe's destruction.
To combat this threat, each world recruits special girls, known as Exceed wielders, to form a defense force.
Saya Sougetsu, a newly awakened Exceed wielder from Earth, joins this force, hoping to make a meaningful impact.
She teams up with Amane Ayashiro, another Earth-based Exceed, and girls from the other worlds to fight against Ouroboros.
The anime follows their journey as they learn to work together and use their unique abilities to protect the universe from impending doom.