The organelle that breaks down sugar molecules (like glucose) to supply energy to the cell is the mitochondrion.

Here's why:

* Mitochondria are the "powerhouses" of the cell. They are responsible for cellular respiration, a process that converts glucose into usable energy in the form of ATP (adenosine triphosphate).

* Cellular respiration occurs in three main stages: glycolysis (occurs in the cytoplasm), the Krebs cycle (occurs in the mitochondrial matrix), and the electron transport chain (occurs on the inner mitochondrial membrane).

* Each stage releases energy, but the majority is produced during the electron transport chain. This energy is used to power various cellular processes.

Let me know if you'd like to learn more about cellular respiration!