It occurred to me to wonder how "angle" came to mean to fish. It seems to have been
based on word for "hook".
angle (v.) - "to fish," 1496, from O.E. angel (n.), related to
anga "hook," from I.E. *ank- "to bend." Figurative sense is
recorded from 1589.
angle (n.) - "intersecting lines," c.1380, from L. angulus
"corner," cognate with from Gk. ankylos "bent, crooked" (see
ankle).