Complex sentence: Angela explains that his father was disappointed that Nathan didn't have the genetic code for special powers so authorized experimentation, reasoning that since everybody in the Petrelli family had powers Nathans body should be able to take it.
Split into simpler sentences: Angela explains that since his father was disappointed that Nathan didn't have the genetic code for special powers, he authorized experimentation on Nathan. The decision was based on the assumption that since everybody else in the Petrelli family had powers, Nathan's body should be able to take it.