  We investigate the magnetic penetration depth \lambda in superconducting
Ba_1-xK_xFe_2As_2 (T_c\simeq32K) with muon-spin rotation (\muSR) and
angle-resolved photoemission (ARPES). Using \muSR, we find the
penetration-depth anisotropy \gamma_\lambda=\lambda_c/\lambda_{ab} and the
second-critical-field anisotropy \gamma_{H_c2} to show an opposite T-evolution
below T_c. This dichotomy resembles the situation in the two-gap superconductor
MgB_2. A two-gap scenario is also suggested by an inflection point in the
in-plane penetration depth \lambda_ab around 7K. The complementarity of \muSR
and ARPES allows us to pinpoint the values of the two gaps and to arrive to a
remarkable agreement between the two techniques concerning the full T-evolution
of \lambda_ab. This provides further support for the described scenario and
establishes ARPES as a tool to assess macroscopic properties of the
superconducting condensate.
