'Wangle' blended word - you say:
To achieve something by scheming or manipulating.
[Of uncertain origin, apparently a blend of wag and dangle.]

If we're guessing, how about 'work angle'?

M-W suggests an alteration of waggle.

edit.-oops my mistake.
My family has used wangle for many years. but I don't see what wag or dangle have to do with the definition.

It would seen that there is an element of "wrangling" in the process of wangling.

Hi pennyless.
I agree but if I pay you your 2 cents worth you'll have to change your name.