An acute angle measures less than 90°. Supplementary angles add up180°, so if one angle is acute (measures less than 90°) the other has to measure more than 90° in order to add up 180°. An angle that measures more than 90° is an obtuse angle, so that is why an angle that is supplementary to an acute angle must be an obtuse angle. Algebraically: x + y = 180 => y = 180° - x => if y < 90° then 180° - x < 90° => x > 180° - 90° => x > 90°.
