Measurement ofB→XγDecays and Determination of|Vtd/Vts|

Using a sample of $383\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ events collected by the BABAR experiment, we measure sums of seven exclusive final states $B\ensuremath{\rightarrow}{X}_{d(s)}\ensuremath{\gamma}$, where ${X}_{d}({X}_{s})$ is a nonstrange (strange) charmless hadronic system in the mass range $0.6--1.8\text{ }\text{ }\mathrm{GeV}/{c}^{2}$. After correcting for unmeasured decay modes in this mass range, we obtain a branching fraction for $b\ensuremath{\rightarrow}d\ensuremath{\gamma}$ of $\mathbf{(}7.2\ifmmode\pm\else\textpm\fi{}2.7(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}2.3(\mathrm{syst})\mathbf{)}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. Taking the ratio of ${X}_{d}$ to ${X}_{s}$ we find $\ensuremath{\Gamma}(b\ensuremath{\rightarrow}d\ensuremath{\gamma})/\ensuremath{\Gamma}(b\ensuremath{\rightarrow}s\ensuremath{\gamma})=0.033\ifmmode\pm\else\textpm\fi{}0.013(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.009(\mathrm{syst})$, from which we determine $|{V}_{td}/{V}_{ts}|=0.177\ifmmode\pm\else\textpm\fi{}0.043$.