I didn't check your work so I'm assuming it's right. The resultant vector is in the third quadrant. Draw the two components so that you can make a right triangle. Now use the fact that tan(x) = (opposite)/(adjacent). Now compute the tan-inverse of this fraction and you'll get the angle. This is not the true angle, but the angle in respect to the quadrant so make sure to add 180 degrees onto it.
Where alpha is the angle(90 here) between two vectors(components in your case ,ie: a and b) and theta the angle of resultant