Let the octagon has x acute angles. So tho sum of these angles is necessarily less than 90x. So the sum of the remaining (8 - x) angles will bo greater than (1080 -90x). Also, the sum of these remaining (8 - x) angles will be less than 180(8 - x). Therefore 1080 - 90x < 180(8 - x) or 90x < 360 Hence, the maximum value of x will be 3.