I know that “to bother” and “to annoy” are synonyms.
Such being the case how will you explain to me the presence of both in the same sentence?
“Don’t bother me with your foolish questions, or I shall be annoyed.”
Thank you for your efforts.
Both Dont bother me, or I shall be bothered. and Dont annoy me, or I shall be annoyed. are truisms and sound silly.
As with many English words they can be synonymous, depending on context, but have subtle difference in meaning. Bothered means a disquiet in mental state, if someone seemed reclusive and thoughtful you would ask "whats bothering you?", you wouldn't ask "whats annoying you?" since they show no signs of annoyance.