Just to get this straight: Angst in German is not Fear, that's "Furcht". Today we tend to use the word "Angst" when we mean "Furcht". Originally, though, Angst in German meant a state of being afraid but without a concrete cause, more like an unspecific uneasiness.

I guess that was the basis for the English use of the word.

Der Mensch ist das edelste Lebewesen. - Das erweist sich schon daraus, dass ihm noch kein anderes widersprochen hat. (G.C. Lichtenberg)