Placate means to calm, appease, or soothe someone who is angry or irritated. The opposite would be to make someone more angry or irritated. 'Exasperate' means to irritate or annoy intensely, making it the correct antonym. 'Disenchant' means to disillusion, 'Advocate' means to support publicly, and 'Implore' means to beg earnestly - none are opposites of placate.