SOLUTION: If 0&#8804;x&#8804;180degrees, find, in degrees, all angles x, which satisfy {{{ (0.2)^(cosx)<1 }}}.

The solution set for this inequality, in the given angle interval, are the angles 

    0 degrees <= x < 90 degrees.



Indeed, if x is in this interval, then  cos(x) is positive, and, hence,    is less than 1.


On contrary,  if  90 degrees < x <= 180 degrees, then cos(x) is negative and, hence,    is greater than 1.


Also notice that the value x= 90 degrees  IS NOT  in the solution set.