I'm not an English teacher but a native speaker.
To understand the term angle: If you look at an object in your hand you are viewing it at a certain angle (front or side etc.). As you turn it over you see it at other angles.
To 'work an angle' (slang) refers to looking at something (an idea not an object) a particular way and using it to your advantage to gain something.
"I can get rid of that angle" could mean the speaker will somehow interrupt the plan or it could mean he's able to kill the person that is "working the angle."
Hope this is helpful!
Student or Learner