Supplement is defined as the other angle that adds up to 180 degrees. So therefore if you have an acute angle you know by definition that the angle is less than 90 degrees. In order for both of them to be supplementary (add up to 180 degrees) the other angle must be greater than 90 degrees. Angles that are greater than 90 degrees are obtuse angles. So an obtuse angle is the supplement of an acute angle.
