나머지 in that sentence means "a result" ~한 나머지 is an idiom means "as a result of ~, so ~ that" 지루한 나머지 means "as a result of boredom" 지루한 나머지 나는 옛 일기장을 꺼내 읽었다. As a result of boredom, I took out my old diaries and read them. I was so boring that I took out my old diaries and read them.

지루한 나머지 나는 옛 일기장을 꺼내 읽었다. This is more like: I was so bored that I took out my old diaries and read them to pass(kill) the time. I took out my old diaries and read them to pass the time. Literal translation: 나는 옛 일기장들을 꺼내 들었고 시간을 보내기(죽이기) 위해 그것들을 읽었다. He took out his old diaries to pass(kill) the time. Maybe he was bored(지루한), but it needs context to be accurate. It is liberally translated. 나머지: 어떤 일의 결과. 예문들: 그는 너무도 어리둥절했던 나머지 정직하게 이야기해 버렸다. 그는 분개한 나머지 한참 동안 말을 잊은 것 같았다. 어머니는 아들의 합격 소식에 너무나 기쁜 나머지 눈물까지 보였다