What enzyme works to add dna to ends of chromosomes in rapidly dividing cells such as those found in an embryo

The correct answer is: telomerase.

Telomeres (ends of chromosomes) shorten during the cell division. Telomerase is an enzyme that has ability to extend the telomeres of chromosomes by adding nucleotides so, they reverse telomere shortening. Telomerase is an RNA-dependent DNA polymerase (it uses RNA as a template for its functioning). Telomerase is active in germ cells because these cells often undergo cell division.