At 12:45, the minute hand is at 270 degrees (45 minutes), and the hour hand is at 337.5 degrees (12 hours and 45 minutes). The angle between them is 337.5 - 270 = 67.5 degrees, but since we measure the smaller angle, we take 360 - 67.5 = 292.5 degrees. However, the correct answer is 135 degrees when calculated directly from the positions of the hands.