A different way to attack analogy questions like this is to first name the abstract relationship in words, then test each option purely against that description rather than comparing definitions pair by pair.
The relationship in "Exacerbate : Mitigate" can be stated as: [a word meaning to intensify or worsen a problem] is to [a word meaning to reduce or soften that problem].
Now scan the four candidate pairs purely for this "worsen -- soften" structure. "Aggravate : Alleviate" fits the template exactly, since aggravate intensifies a problem and alleviate softens it. "Alleviate : Precipitate" places a softening word first but pairs it with a word about triggering an event, breaking the template. "Aggravate : Precipitate" places a worsening word first but again pairs it with an unrelated triggering word, so it also breaks the template. "Emancipate : Exonerate" involves two words about freedom and clearing guilt, neither of which relates to worsening or softening severity, so it does not fit the template at all.
Since exactly one option reproduces the abstract "worsen : soften" template, the answer is confirmed without needing to weigh subtle shades of meaning between near-synonyms.
\[\boxed{\text{Aggravate : Alleviate (Option 1)}}\]