Half-Elves were a hybrid species that were a cross between an elf and a human. Eragon was given elf-like features and abilities by the dragons, but he was not truly a half-elf.
Existence
Half-elves have never been specifically reference within the books of the Inheritance cycle. However, during an interview with Christopher Paolini on Shur'tugal.com Paolini said that: "They have existed, although most weren't able to have children of their own. As for whether any exist now; let's just say that if they do, they would have become very, very skilled at blending in with whatever race (elves or humans) they had chosen to live among. Half-elves, half-humans have much-extended life spans, but they aren't immortal like full-blooded elves." [1]
It is possible that Angela might be half-elven, as she is apparently older than she looks and is respected by elves.