Final answer:
Lysosomes are the organelles responsible for storing sugar as glycogen and breaking it down into glucose subunits with their digestive enzymes.
Step-by-step explanation:
The structures that store sugar in the form of glycogen and contain enzymes to degrade glycogen into its glucose subunits are known as lysosomes.
Lysosomes are membrane-bound organelles containing a suite of digestive enzymes including those necessary for the breakdown of glycogen.
They play a critical role in digesting excess or stored cellular components as well as foreign material, which makes them essential for cellular homeostasis and defense.
Unlike peroxisomes, which carry out oxidation reactions and detoxify poisons, or glycosomes, which are involved in storing and converting fat into sugar in plants, lysosomes are primarily responsible for degradation and recycling processes within animal cells.