When one is filled with incredible rage, but just too lazy to actually do anything about it. So one might swear or move an few feet away from the source of one's mangriness. Often accompanied by a forceful "MEH!" noise.
My cat gets really mangry if I poke him when he's trying to sleep.
Mangry is a type of angryness. However it is felt by some that angry can mean too much of a variety of things and so is now seen as being 'femininly' angry. eg, bitching, silent treatment etc. Mangry is 'man angry' bang your fist on the table angry. I'm going to kill him angry. shouting and swearing and kicking stuff angry.
I'm going to kill him im so mangry!!
Man, im so mangry i could just punch you!!
I'm not just angry, im MANGRY!!