Final answer:
The nucleus is the organelle in eukaryotic cells that packages X-shaped chromosomal material, which consists of linear chromosomes bundled as chromatin.
Step-by-step explanation:
The organelle in eukaryotic cells that packages the X-shaped chromosomal hereditary material is the nucleus. Unlike eukaryotes, prokaryotic cells do not have a nucleus; instead, their DNA is organized into a single circular chromosome in an area of the cytoplasm called the nucleoid.
Eukaryotic DNA is made up of chromosomes that are linear structures housed within the nucleus. The eukaryotic chromosomes are bundled with proteins to form structures known as chromatin, which can be further condensed into visible chromosomes during cell division.