We can drop a perpendicular bisector in the triangle, splitting the vertex angle up into 21 degrees and 21 degrees. (And thus we have two right triangles).
Using Law of Sines:
(Sin90)/12 = (Sin21)/b
Solve for b:
b = 11.2303
Thus, the total base is 22.4606
Nevermind, I just realized you wanted to find just the base angles; this is easy from just subtracting each angle 180 - 21 - 90 = 69 degrees, and obviously each of the base angles will be congruent since it's an isosceles triangle.