Learn Spanish (Latin America): Dicen que los ángeles existen.

This is an example of the "impersonal they." There is no specific group of people being referred to; it’s just the standard Spanish way of saying "people say" or "it is said." If you added ellos to make it ellos dicen que..., it would sound like you are talking about a specific group of people you previously mentioned.

Why do we need the article los before ángeles? In English, we just say "angels exist."

In Spanish, when you talk about a noun in a general, all-encompassing sense (like the concept of angels in general), you must use a definite article (el, la, los, las). While English drops the "the" for general plural nouns, Spanish requires it.

Why doesn't dicen que trigger the subjunctive here?

When decir is used to report information, state a belief, or declare something, the following verb takes the indicative mood (existen). You only use the subjunctive with decir when it acts as a command or a request (e.g., "They tell the angels to leave").

Why does ángeles have an accent mark?

The spoken stress of the word falls on the third-to-last syllable (án-ge-les). In Spanish, any word stressed on the third-to-last syllable is called an esdrújula word, and it always requires a written accent mark.