Given lines are $2 x+11 y-7=0$
and $ x+3 y+5=0 $
$\Rightarrow y=-\frac{2}{11} x+\frac{7}{11}$
and $y=-\frac{1}{3} x-\frac{5}{3}$
Their, slopes are
$m_{1}=-\frac{2}{11}$
and
$m_{2}=-\frac{1}{3}$
$\therefore $ Angle between lines is
$\tan \theta =\frac{m_{1}-m_{2}}{1+m_{1} m_{2}}$
$=\frac{-\frac{2}{11}+\frac{1}{3}}{1+\frac{2}{11} \times \frac{1}{3}}=\frac{-6+11}{33+2}=\frac{5}{35}$
$\Rightarrow \theta=\tan ^{-1}\left(\frac{1}{7}\right)$