  Magnetic-field-angle-resolved heat capacity of dimer-Mott organic
superconductors $\kappa$-(BEDT-TTF)$_2$$X$ is reported. Temperature and field
dependence of heat capacity indicates that the superconductivity has line nodes
on the Fermi surface, which is a typical feature of $d$-wave superconductivity.
In-plane field-angle dependence exhibits fourfold oscillations as well as
twofold oscillations due to anisotropy of superconducting gap functions. From
analyses of the fourfold term, the gap symmetry is determined as
$d_{x^{2}-y^{2}}$+$s_{\pm}$ for $X$=Cu[N(CN)$_2$]Br and $d_{xy}$ for
$X$=Ag(CN)$_2$H$_2$O. We suggest that the symmetry difference comes from the
competition of $d_{xy}$ and $d_{x^{2}-y^{2}}$ antiferromagnetic fluctuations
depending on lattice geometry.
