In a way that shows you are annoyed and have lost your patience — not sudden hot anger, but the tired, fed-up kind that builds after something has gone wrong again and again. If you say something exasperatedly, people can hear it: a sigh first, a flat or sharp voice, maybe the same question asked one more time ("Why do I have to tell you every single day?"). It is a written word more than a spoken one — you will meet it in stories, telling you how a character spoke, right next to said, sighed, asked. In real conversation people just say "he sounded really fed up". It also goes with actions that leak the same feeling: throw up your hands exasperatedly, shake your head exasperatedly. One useful thing about it: it usually points at a person who keeps doing something, not at bad luck. You are exasperated with your little brother, less naturally with the rain.