In intermediate polars (IPs), the intrinsic thermal emissions from white dwarfs (WDs) have typically been studied. Few reports have analyzed X-ray reflections from WDs. We recently developed an elaborate IP-reflection spectral model. Herein, we report the first application of a reflection model with an IP thermal model to the spectra of the brightest typical IP V1223 Sagittarii observed by the Suzaku and NuSTAR satellites. The model reasonably reproduces the spectra within the range of 5-78 keV and estimates the WD mass as 0.92$pm$0.02 $M_odot$. The WD mass estimated by the proposed model is consistent with that measured using an active galactic nuclei reflection model and a partial covering absorption model. However, the choice of incorrect parameter values, such as an unsuitable fitting energy band and an incorrect metal abundance, was found to introduce systematic errors (e.g., $<sim$ 0.2 $M_odot$ in the WD mass) in the WD mass measurement. Our spin phase-resolved analysis resulted in discoveries regarding the modulations of the equivalent width of the fluorescent iron K$_{alpha}$ line and the angle between the post-shock accretion column and the line-of-sight (viewing angle). The viewing angle anti-correlates approximately with the X-ray flux and has average and semi-amplitude values of 55$^circ$ and 7$^circ$, respectively, which points toward two WD spin axis angles from the line-of-sight of 55$^circ$ and 7$^circ$, respectively. Both estimated spin axis angles are different from the reported system inclination of 24$^circ$.
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