Which of these sentences is written correctly?
- Angela has three brothers, Mark, Adam, and Ryan.
- Angela has three brothers: Mark, Adam, and Ryan.
- Angela has three brothers Mark, Adam, and Ryan
That's the one to go with.
N.B. This is called the syntactical-descriptive function of the colon: it "introduces a description—in particular, makes explicit the elements of a set" (Wikipedia)
In a series of three or more terms with a single conjunction, use a comma after each term except the last. With only a few exceptions, the serial comma clarifies any ambiguity when the meaning is not as simple as the example above. Clarity ought to be the objective in writing!