Is the supplement of an acute angle is an obtuse angle

Yes. Supplementary angle is one which when added to the angle makes 180 degrees. Thus, if the angle is acute, its supplementary angle would be obtuse.

The statement is always true because the sum of the two angles must be 180 degrees to be supplementary. If the first angle is an acute angle, then it has a measure of less than 90 degrees. To sum 180 degrees, the second angle would need to be more than 90 degrees, making it an obtuse angle.