### Why is the supplement of an acute angle always obtuse?

An acute angle is an angle that is between 0 and 90 degrees. The supplement of the angle is 180 degrees minus the magnitude of the angle. Since the original angle is greater than 0 degrees, the supplement must be less than 180-0 = 180 degrees. Since the original angle is less than 90 degrees, the supplement must be greater than 180-90 = 90 degrees. Thuis, the supplement measures between 90 and 180 degrees…