Option 1: Provoke -> means to deliberately anger or irritate someone, which is the opposite of calming them down.
Option 2: Appease -> is actually a synonym of placate, both mean to calm or pacify someone.
Option 3: Hate -> is an emotion of intense dislike, not an action opposite to soothing someone.
Option 4: Nullify -> means to make invalid or cancel out, unrelated to calming or angering.
Hence, Option 1: Provoke -> PLACATE means to calm or soothe someone who is angry, while PROVOKE means to deliberately cause anger or annoyance, making them perfect antonyms -> correct