Question

You tell a friend, “you must be busy. i'd better let you go,” because you want out of the conversation. what type of lie did you use?

Answer 1

The type of lie that you use in this situation is: Hinting

Hinting is a type of lie by not directly said a lie but by passively influencing someone to choose a decision by revealing specific information.
Another example of hinting: saying "You must be a lot fitter than me. I guess i wouldn't be able to keep up with you on the hiking trip" as a way to avoid going hiking with your friends.