Liquid interfaces, capillarity and self-assembly of particles at interfaces are important in nature and technology. When a particle is adsorbed to a liquid interface, the contact line of the particle with the liquid interface and the associated contact angle are the crucial parameters that drive assembly of the particles. We looked at how the shape of the liquid interface and the shape of the particle affect the contact angle and the shape of the contact line. We used millimeter-sized PDMS-coated glass spheres and measured the contact angles at isotropic (planar) and anisotropic interfaces (saddle and cylindrical in shape). Anisotropy of the liquid interface is defined by the deviatoric curvature D0. We look at the apparent advancing and receding contact angles (qA, qR) separately. We found that as the anisotropy of the interface, D0, increased from 0 to 0.22mm-1, the apparent receding angle, qR, decreased from 101° to 80°. Over the same experiments, qA remained fixed at 109°. As D0 increases, we also find that the contact line around the sphere deforms. We make analogy to electrostatics to describe the shape of the contact line in terms of multipole moments. We measured that as D0 increased, the magnitude of the quadrupolar moment (z2) increased and qR decreased. Magnitudes of z2 measured in our experiments agree with previous predictions when capillary force is zero. We also measure the z2 with applied capillary force. However, there is no theory to compare it. To our knowledge, this is the first time that quadrupolar deformation of contact line around a particle is observed and measured directly. Moreover, we showed that advancing and receding contact angles of anisotropic shaped solids, such as cylinders, differ at a planar interfaces, which we attribute to the deformation of the contact line. Our results bring a new perspective to contact angles, showing that the advancing and receding angles depend on liquid-interface geometry, which had not previously been appreciated. Thus, our results are broadly important for capillarity and self-assembly related problems.