member of a Teutonic tribe, Old English, from Latin Angli "the Angles," literally "people of Angul" (Old Norse Öngull), a region in what is now Holstein, said to be so-called for its hook-like shape (see angle (n.)). Or the name might refer to fishing (with hooks) as a main activity of the people, and Proto-Germanic *anguz is said also to have meant "narrow," so it might refer to shallow coastal waters.
People from the tribe there founded the kingdoms of Mercia, Northumbia, and East Anglia in 5c. Britain. Their name, rather than that of the Saxons or Jutes, may have become the common one for the whole group of Germanic tribes because their dialect was the first committed to writing.
Figurative sense "point or direction from which one approaches something" is from 1872. Angle-bracket is 1781 in carpentry; 1956 in typography.