The word apoplectic has multiple origins, potentially borrowed from French ("apoplectique") or Latin ("apoplēcticus"), but it ultimately derives from the Greek verb "apoplēssein" (ἀποπλήσσειν), ‘to cripple or disable by a stroke’.   It initially meant "of or relating to or causing apoplexy," which at the time referred to a sudden illness causing paralysis and dizziness (a stroke). By the 1720s, the meaning evolved to "showing signs of apoplexy," eventually leading to its current informal sense of "extremely angry" or "enraged". 

According to the Oxford English Dictionary (OED), the earliest known use of the word "apoplectic" in English is from before 1625, in a text written by playwrights Francis Beaumont and John Fletcher. 

Examples of "apoplectic" used in a sentence:  
"She was positively apoplectic with anger when she realized she had been cheated." 
"Some of the people in the political universe are apoplectic on the subject."
"The base of her party has been apoplectic for the better part of three years." 
"The victim’s family was apoplectic when the case against their son’s killer was dismissed." 
"When the cashier refused to give me the correct change, I became apoplectic and threatened to call the police."
"The apoplectic husband threatened to kill his wife’s lover."
"Because Matt always appears apoplectic, he is being forced to take an anger management course by the traffic court judge."