How does Angel have a brain the size of a planet?

Solution 1:

As mentioned by djsmiley2k in the comments, this is indeed just an Easter egg statement in reference to the 'Hitchhikers Guide to the Galaxy'.

In the second Lost ECHO recording detailing Zer0's backstory, Handom Jack tells Angel she's "got a brain the size of a planet", which is reference to Marvin the depressed android's "brain the size of a planet" lament.

Reference

Looking at Jack's statement in regards to what it means about Angel you would think that it is referencing the fact that her Siren power is "Artificial Intelligence". Her father Jack is also a programmer for Hyperion which may be related the reason she has the power of Artificial Intelligence.

Some Background Information on Angel

Solution 2:

Angel has a neural interface that networks her with all the Hyperion computers on Pandora.

You can see this throughout the Borderlands games, when she speaks through and exerts direct control over computers.

So, although the statement is not literally true in regards to the organic brain in her skull, Angel effectively has a brain the size of a planet, because her neural network covers Pandora's surface (as well as satellites in orbit).