納得(なっとく)がいくto understand and accept as valid (of a thought, action, etc.), to be satisfied with

データを見(み)て理論(りろん)に納得(なっとく)がいきました。

After looking at the data, I was able to understand and accept the theory as valid. {to understand and accept as valid (of a thought, action, etc.), to be satisfied with}

納得(なっとく)がいく説明(せつめい)を聞(き)いたので質問(しつもん)はありません。

I have no questions because I heard an explanation that I understand and accept as valid. {to understand and accept as valid (of a thought, action, etc.), to be satisfied with}

よく遅刻(ちこく)をする社員(しゃいん)が昇給(しょうきゅう)することに納得(なっとく)がいかない。

I cannot understand and accept that an employee who often arrives late gets a raise. {to understand and accept as valid (of a thought, action, etc.), to be satisfied with}

説明(せつめい)を聞(き)いても納得(なっとく)がいかなかったのか、彼女(かのじょ)は僕(ぼく)の意見(いけん)に反対(はんたい)した。

Even after listening to the explanation, she disagreed with my opinion; perhaps she wasn't able to understand and accept it as valid. {to understand and accept as valid (of a thought, action, etc.), to be satisfied with}

仕事(しごと)で納得(なっとく)がいかない事(こと)がいくつもあり、ついに怒(いか)りが爆発(ばくはつ)してしまった。

There were several things at work that I couldn't understand and accept as valid, which eventually led to an explosion of anger. {to understand and accept as valid (of a thought, action, etc.), to be satisfied with}