180 degrees.
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The minute hand passes through 360 degrees in an hour and 6 degrees in a minute
1/6 of half a rotation = 1/12 of a rotation = 1/12 of 360 degrees = 360/12 = 30 degrees.
The angle between the hour hand and the minute hand on a standard clock at 6:30 is 15 degrees. Let's review the movement of the hands of the clock specific to this problem. The hour hand moves through the 12 hours of half a day in 12 hours (naturally), and that translates into the hour hand moving 360 degrees in 12 hours. That means the hour hand moves 360/12, or 30 degrees per hour. That translates into 15 degrees in half an hour. If the hour hand is pointing straight down at 6:00 (which it is), it will move 15 degrees from where it was in half and hour. And the time will be 6:30 with the minute hand pointing straight down. The minute hand will be pointing to where the hour hand was half an hour ago. And, as stated, the hour hand will have moved from dead on the six and gone 15 degrees further around.
From 12pm to 2:30pm, the hour hand goes 75 degrees. It is the minute hand that goes through 795 degrees.
6 degrees