The angle between the lines $\frac{x-2}{3}=\frac{y+1}{-2}, z = 2$ and $\frac{x-1}{1}=\frac{2y+3}{3}=\frac{z+5}{2}$ is 

$\frac{\pi}{2}$

The given equations are not in standard form. The equations of the given lines in standard form can be written as

$\frac{x-2}{3}=\frac{y+1}{-2}=\frac{z-2}{0}$ ...........(i)

and, $\frac{x-1}{1}=\frac{y+3/2}{3/2}=\frac{z+5}{2}$ .............(ii)

If $\theta $ is the angle between the givem lines, then 

$cos \theta = \frac{(3)(1)+(-2)(3/2)+(0)(2)}{\sqrt{3^2+(-2)^2+0^2}\sqrt{1^2+(3/2)^2+2^2}}=0$

$⇒ \theta = \frac{\pi}{2}$