Using a sample of 1.06×108ψ(3686) events produced in e+e- collisions at s=3.686 GeV and collected with the BESIII detector at the BEPCII collider, we present studies of the decays ψ(3686)→K-ΛΞ¯++c.c. and ψ(3686)→γK-ΛΞ¯++c.c.. We observe two hyperons, Ξ(1690)- and Ξ(1820)-, in the K-Λ invariant mass distribution in the decay ψ(3686)→K-ΛΞ¯++c.c. with significances of 4.9σ and 6.2σ, respectively. The branching fractions of ψ(3686)→K-ΛΞ¯++c.c., ψ(3686)→K-Σ0Ξ¯++c.c., ψ(3686)→γχcJ→γK-ΛΞ¯++c.c. (J=0, 1, 2), and ψ(3686)→Ξ(1690/1820)-Ξ¯++c.c. with subsequent decay Ξ(1690/1820)-→K-Λ are measured for the first time.