Learn German: Das Monster existiert angeblich nicht. - The monster supposedly does not exist.

You can rewrite it as Das Monster soll nicht existieren. Using the adverb angeblich (supposedly) is simply an alternative way to express rumors. When you use sollen, it takes the second position as the conjugated verb, and the main verb existieren moves to the end as an infinitive.

Why does nicht come after angeblich instead of before it?

In German, when nicht negates the entire action (the fact that the monster exists), it gets pushed to the end of the clause, coming after adverbs like angeblich. If you said nicht angeblich, you would be negating the word supposedly rather than negating the existence of the monster.

Does using angeblich mean the speaker believes the monster exists?

No, it usually implies the exact opposite. Just like the subjective use of sollen, adding angeblich distances the speaker from the statement. It signals that this is just a rumor or claim, and the speaker likely doubts it.

Can I use angeblich in everyday conversation, or is it strictly formal?

You can absolutely use it in daily conversation! While you will hear it on the news to mean allegedly, Germans use angeblich all the time in casual speech to mean supposedly or to express skepticism about gossip.