Angler, Angling

What is the connection between angling and angles?
 
The noun angler, from the mid-15th century, refers to a fisher who uses a hook and line. In the 14th century, Angler was a surname. An angler is someone who goes angling.
 
The verb ‘to angle’ (to fish with a hook), from the mid-15th century, is from Old English angel (angle, hook, fish-hook) and Old English anga (hook), from Proto-Germanic angul and the Proto-Indo-European (PIE) root ank (to bend).
 
The use of ‘to angle’ meaning to catch or elicit by artful wiles is from the 1580s. For example, the clever person was able to wile their way unseen into the building; or, a wily person used all their wiles to get a bargain on the used car.
 
The noun angle, from the late 14th century, a space or difference in direction between intersecting lines, is from Old French angle (angle, corner), Latin angulus (angle, corner), and the PIE root ank (to bend).
 
In brief, the word angle in reference to fishing comes to English from Germanic sources whereas the word angle in reference to math comes to English from Latin and French sources. Both sources have their origin in variations of PIE ank.
 
Reference: Online Etymological Dictionary, https://www.etymonline.com/