We investigate the magnetic penetration depth lambda in superconducting Ba1-xKxFe2As2 (Tc approximately 32 K) with muon-spin rotation (microSR) and angle-resolved photoemission (ARPES). Using microSR, we find the penetration-depth anisotropy gamma lambda=lambda c/lambda ab and the second-critical-field anisotropy gammaHc2 to show an opposite T evolution below Tc. This dichotomy resembles the situation in the two-gap superconductor MgB2. A two-gap scenario is also suggested by an inflection point in the in-plane penetration depth lambda ab around 7 K. The complementarity of microSR 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 lambdaab. This provides further support for the described scenario and establishes ARPES as a tool to assess macroscopic properties of the superconducting condensate.