Green's Dictionary of Slang gives this definition of "hang," referring to turning left or right in a car, with a citation from 1966.
(orig. US) to turn a corner in a motorcar; as in hang a left, hang a right.
There are many earlier uses of the phrase "hang a left" and "hang a right," but they appear to mostly refer to throwing a punch with the left or right arm respectively, especially in boxing, but sometimes applying outside of sport.
In these cases, it is often described as a left or right "hook," or "jab," as in hang a left hook or hang a left jab.
I haven't found this sense defined in either the OED or in GDoS, but citations are not hard to find.
Berg hangs a left jab on Tony's ear in the seventh
-1931 - Daily News (New York, NY) 11 Sep (paywall)
Sometimes, this sense is also used without a following object like "hook" or "jab," as with "hanging a left" in your car, a boxer can "hang a left" on their opponent and the meaning is clear.
Richard Li Brandi... hangs a left on jaw of Lawrence Greene
- 1934 - Daily News (New York, NY) 20 Mar (paywall)
Based on my research, it appears that throw a left hook is the most common term in boxing for referring to a punch, with hang perhaps being more colloquial.
What sense of the word "hang" is being used in boxing when it refers to a punch? Is it slang that developed exclusively in boxing, or does this notion of "hanging" meaning throwing a punch go back further, or exist in other domains?
Did this "hang a [direction]" pattern have any influence on the more recent slang for turning right or left in a car, or are the two senses of the word "hang" in any way related?