Final answer:
The property of electron-degenerate matter that is important in the evolution of a star is that this type of matter is highly dense and composed of electrons. At extreme densities, known as degenerate matter, the electrons resist being pushed closer together and set up a powerful pressure inside the core, which is important in determining the evolution of stars.
Step-by-step explanation:
The property of electron-degenerate matter that is important in the evolution of a star is that this type of matter is highly dense and composed of electrons. When a star exhausts its store of nuclear energy and begins its final collapse, the core contracts and the electrons are squeezed closer together. At extreme densities, known as degenerate matter, the electrons resist being pushed closer together and set up a powerful pressure inside the core, which is important in determining the evolution of stars.