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Analysis of the transit light curve deformed by the stellar gravity darkeningallows us to photometrically measure both components of the spin-orbit angle$\psi$, its sky projection $\lambda$ and inclination of the stellar spin axis$i_\star$. In this paper, we apply the method to two transiting hot Jupitersystems monitored with the Kepler spacecraft, Kepler-13A and HAT-P-7. ForKepler-13A, we find $i_\star=81^\circ\pm5^\circ$ and $\psi=60^\circ\pm2^\circ$adopting the spectroscopic constraint $\lambda=58.6^\circ\pm2.0^\circ$ byJohnson et al. (2014). In our solution, the discrepancy between the above$\lambda$ and that previously reported by Barnes et al. (2011) is solved byfitting both of the two parameters in the quadratic limb-darkening law. We alsoreport the temporal variation in the orbital inclination of Kepler-13Ab,$\mathrm{d} |\cos i_{\rmorb}|/\mathrm{d}t=(-7.0\pm0.4)\times10^{-6}\,\mathrm{day}^{-1}$, providingfurther evidence for the spin-orbit precession in this system. By fitting theprecession model to the time series of $i_{\rm orb}$, $\lambda$, and $i_\star$obtained with the gravity-darkened model, we constrain the stellar quadrupolemoment $J_2=(6.1\pm0.3)\times10^{-5}$ for our new solution, which is severaltimes smaller than $J_2=(1.66\pm0.08)\times10^{-4}$ obtained for the previousone. We show that the difference can be observable in the future evolution of$\lambda$, thus providing a possibility to test our solution with follow-upobservations. The second target, HAT-P-7, is the first F-dwarf star analyzedwith the gravity-darkening method. Our analysis points to a nearly pole-onconfiguration with $\psi=101^\circ\pm2^\circ$ or $87^\circ\pm2^\circ$ and thegravity-darkening exponent $\beta$ consistent with $0.25$. Such anobservational constraint on $\beta$ can be useful for testing the theory ofgravity darkening.

Spin-Orbit Angles of Kepler-13Ab and HAT-P-7b from Gravity-Darkened Transit Light Curves