  When a phase-separated binary ($A+B$) mixture is exposed to a wall, that
preferentially attracts one of the components, interfaces between A-rich and
B-rich domains in general meet the wall making a contact angle $\theta$.
Young's equation describes this angle in terms of a balance between the $A-B$
interfacial tension $\gamma_{AB}$ and the surface tensions $\gamma_{wA}$,
$\gamma_{wB}$ between, respectively, the $A$- and $B$-rich phases and the wall,
$\gamma _{AB} \cos \theta =\gamma_{wA}-\gamma_{wB}$. By Monte Carlo simulations
of bridges, formed by one of the components in a binary Lennard-Jones liquid,
connecting the two walls of a nanoscopic slit pore, $\theta$ is estimated from
the inclination of the interfaces, as a function of the wall-fluid interaction
strength. The information on the surface tensions $\gamma_{wA}$, $\gamma_{wB}$
are obtained independently from a new thermodynamic integration method, while
$\gamma_{AB}$ is found from the finite-size scaling analysis of the
concentration distribution function. We show that Young's equation describes
the contact angles of the actual nanoscale interfaces for this model rather
accurately and location of the (first order) wetting transition is estimated.
