An optical analog of the quantum weak measurement scheme proved to be very useful for the observation of optical beam shifts. Here we adapt the weak value amplification method to the observation of the angular Goos-Hänchen shift. We observe this effect in the case of external air-dielectric reflection, the more fundamental case in which it occurs. We show that weak measurements allow for a faithful amplification of the effect at any angle of incidence, even at Brewster's angle of incidence.