Transport measurements are presented on a quantum ring that is tunnel-coupled to a quantum dot. When the dot is in the Coulomb blockade regime, but strongly coupled to the open ring, Fano line shapes are observed in the current through the ring, when the electron number in the dot changes by 1. The symmetry of the Fano resonances is found to depend on the magnetic flux penetrating the area of the ring and on the strength of the ring-dot coupling. At temperatures above T=0.65 K the Fano effect disappears, while the Aharonov-Bohm interference in the ring persists up to T=4.2 K. Good agreement is found between these experimental observations and a single-channel scattering matrix model including decoherence in the dot.