\[\boxed{\mathbf{360}\mathbf{.}}\]
\[1)\ \frac{1}{7}x = \frac{5}{6}\]
\[x = \frac{5}{6}\ :\frac{1}{7}\]
\[x = \frac{5}{6} \cdot 7\]
\[x = \frac{35}{6}\]
\[x = 5\frac{5}{6}.\]
\[2)\ \frac{4}{15}\ :x = 8\]
\[x = \frac{4}{15}\ :8\]
\[x = \frac{4}{15} \cdot \frac{1}{8}\]
\[x = \frac{1}{30}.\]
\[3)\ 1\frac{4}{9}x = 5\frac{1}{5}\]
\[x = \frac{26}{5}\ :\frac{13}{9}\]
\[x = \frac{26}{5} \cdot \frac{9}{13}\]
\[x = \frac{26 \cdot 9}{5 \cdot 13}\]
\[x = \frac{18}{5}\]
\[x = 3\frac{3}{5}.\]