  The equilibrium contact angle of a droplet resting on a solid substrate can
reveal essential properties of the solid's surface. However, when the motion of
a droplet on a surface shows significant hysteresis, it is generally accepted
that the solid's equilibrium properties cannot be determined. Here, we describe
a method to measure surface tensions of soft solids with strong wetting
hysteresis. With independent knowledge of the surface tension of the wetting
fluid and the linear-elastic response of the solid, the solid deformations
under the contact line and the contact angle of a single droplet together
reveal the difference in surface tension of the solid against the liquid and
vapor phases. If the solid's elastic properties are unknown, then this surface
tension difference can be determined from the change in substrate deformations
with contact angle. These results reveal an alternate equilibrium contact
angle, equivalent to the classic form of Young-Dupr\'{e}, but with surface
tensions in place of surface energies. We motivate and apply this approach with
experiments on gelatin, a common hydrogel.
