2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130179We give an identity involving sums of functions of lengths of simple closed geodesics, known as a McShane identity, on any non-orientable hyperbolic surface with boundary which generalises Mirzakhani's identities on orientable hyperbolic surfaces with boundary.23 pages; improved description of the moduli spaceGeometric TopologyDifferential Geometry32G15; 58D27; 30F60text