How many degrees does the hour hand move from 3:00 to 5:30?

now, keeping in mind that a circular clock has 360° total, and there are 12 hours labeled on it evenly, so the angle between each hour label is 360 : 12 = 30.

so, from 3pm to 5pm, it moved by 30° + 30° = 60°.

from 5pm to 5:30, that's only half an hour, so it moved half 30°, or 15°.

60° + 15° = 75°.