Acute angle, in radians  between the lines whose slope is 2 and the line which is perpendicular to the line $2\mathrm{x}-\mathrm{y}+5=0$  is

The slope of the line  $2\mathrm{x}-\mathrm{y}+5=0$  is $\mathrm{m}=-\frac{\mathrm{a}}{\mathrm{b}}=2$  , it is same as the slope of the first line. 
Hence the angle between the line whose slope is 2 and the line which is perpendicular to the line $2\mathrm{x}-\mathrm{y}+5=0$   is   $\frac{\pi }{2}=\boxed{1.57}$