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Radial velocity (RV) measurements of transiting multiplanet systems allow us to understand the densities and compositions of planets unlike those in the Solar System. Kepler-102, which consists of 5 tightly packed transiting planets, is a particularly interesting system since it includes a super-Earth (Kepler-102d) and a sub-Neptune-sized planet (Kepler-102e) for which masses can be measured using radial velocities. Previous work found a high density for Kepler-102d, suggesting a composition similar to that of Mercury, while Kepler-102e was found to have a density typical of sub-Neptune size planets; however, Kepler-102 is an active star, which can interfere with RV mass measurements. To better measure the mass of these two planets, we obtained 111 new RVs using Keck/HIRES and TNG/HARPS-N and modeled Kepler-102's activity using quasi-periodic Gaussian Process Regression. For Kepler-102d, we report a mass upper limit of M$_{d} < $5.3 M$_{\oplus}$ [95\% confidence], a best-fit mass of M$_{d}$=2.5 $\pm$ 1.4 M$_{\oplus}$, and a density of $ρ_{d}$=5.6 $\pm$ 3.2 g/cm$^{3}$ which is consistent with a rocky composition similar in density to the Earth. For Kepler-102e we report a mass of M$_{e}$=4.7 $\pm$ 1.7 M$_{\oplus}$ and a density of $ρ_{e}$=1.8 $\pm$ 0.7 g/cm$^{3}$. These measurements suggest that Kepler-102e has a rocky core with a thick gaseous envelope comprising 2-4% of the planet mass and 16-50% of its radius. Our study is yet another demonstration that accounting for stellar activity in stars with clear rotation signals can yield more accurate planet masses, enabling a more realistic interpretation of planet interiors.