We investigate the magnetic penetration depth lambda in superconducting Ba_1-xK_xFe_2As_2 (T_csimeq32K) 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.
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