-(으)ㄴ/는 나머지 means "as a result of" - excessive action causing outcome.
Excessive cause - 너무 기쁜 나머지 울었어요 (cried from being too happy)
Overflow - Emotion/action so strong it caused something
Result of intensity - Too much of X led to Y
See examples below for varied real-world usage.
Usually with emotional or intense actions
나머지 = remainder/rest
I was so surprised that I couldnt speak.
I was so happy to hear the news of passing that I burst into tears.
I was so absorbed in the game that I forgot about the appointment time.
I was so tired yesterday that I couldn't even wash up and just fell asleep.
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