The 2HDM+S is the singlet extension of the two-Higgs-doublet model (2HDM). The singlet field and its mixing with the 2HDM Higgs sector lead to new contributions to the electroweak precision observables, in particular, the oblique parameters. In this study, we performed a systematic investigation of the impacts of each mixing angle on the oblique parameters. We adopted the mixing angles and physical Higgs masses as our parameters, which allow a mapping when a specific symmetry structure of the Higgs potential and various theoretical considerations are taken into account. We identified five benchmark cases, where at most one mixing angle was nonzero, and analyzed the 95% C.L. allowed parameter space using the oblique parameters. In the alignment limit of the 2HDM, we find that, other than the usual mass relations of $m_H\sim m_{H^\pm}$ or $m_A\sim m_{H^\pm}$ , electroweak precision measurements also impose an upper limit on the neutral Higgs masses. In the cases with nonzero singlet mixing with the 2HDM Higgses $\textit{H}$ or $\textit{A}$, we find approximate mass relations of $c^2_{\alpha_{HS}} m_{H} + s^2_{\alpha_{HS}}m_{h_S} = m_{H^\pm}$ or $c^2_{\alpha_{AS}} m_{A} + s^2_{\alpha_{AS}}m_{A_S} = m_{H^\pm}$ . These relations are universal to the 2HDM+S models, with or without further symmetry assumption. We also studied the non-alignment limit of the 2HDM+S, which typically has tighter constraints on the masses and mixing angles. Finally, we examined the complementarity between the electroweak precision analyses and the Higgs coupling precision measurements.