This is the 664th most frequent Turkish word.
açtığı
The Turkish word "açtığı" means "that he/she/it opened" or "which he/she/it opened," depending on the context.
The word "açtığı" here works as a relative participle, describing the door that he opened.
O, açtığı kapıdan hızlıca geçti.
He quickly passed through the door he opened.
Here, "açtığı" is used to describe an event action, 'he opened/the exhibition inaugurated.'
Onun açtığı sergi büyük ilgi gördü.
The exhibition he inaugurated received great attention.
In this sentence, "açtığı" indicates a result or effect stemming from an action, 'having opened/problems arising'.