Answer:127.5∘
Explanation:
The angle measure between any two consecutive numbers on a clock is 36012=30∘.
Call the "12" point on the clock the zero-degree point.
At 4:45, the minute hand is at the "9" - that is, at the 30×9=270∘ mark. The hour hand is three-fourths of the way from the "4" to the "5; that is,
30×434=142.5∘ mark.
Therefore, the angle between the hands is
270−142.5=127.5∘, the desired measure.