\ensuremath{\alpha}-particle evaporation spectra and $\ensuremath{\gamma}$-ray multiplicities were measured for various target-projectile systems corresponding to residual nuclei in the range of ${Z}_{R}=48\text{\ensuremath{-}}55$ and with excitation energy in the range of 30--40 MeV. The high-energy part of the evaporation spectra were analyzed using the statistical model code PACE2 to derive values of the inverse level-density parameter $(K)$. The $K$ values were found to be in the range of 9.0--10.5 for all systems. Angular momentum dependence of the inverse level-density parameter was investigated using the $\ensuremath{\gamma}$-ray multiplicity data. It is seen that there are strong variations in $K$ as a function of angular momentum for many systems. Present results provide important input information for a systematic understanding of the statistical properties of nuclei at moderate excitation energies and angular momenta.