Question 890669
Since both the minute hand and the our hand are
moving all the time, their rates of motion have to 
be taking into account.
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One full circle is {{{ 60 }}} minutes
The circular rate of motion of the minute hand is 
{{{ 60 }}} min / hr
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The circular rate of motion of the hour hand is
{{{ 5 }}} min / hr ( from 12 to 1 AM in one hour )
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At 1 AM, the fraction of the circle between the hands is
{{{ 5/60 = 1/12 }}}
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While the minute hand goes from the 12 position to
{{{ 48 }}} minutes after, the fraction of the circle is:
{{{ 48/60 = 4/5 }}} ( in terms of a 60 minute full circle )
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Since the hour hand travels at {{{ 5/60 = 1/12 }}} of
the rate of the minute hand,
It's angle traveled is:
{{{ (1/12)*(4/5) = 4/60 }}}
{{{ 4/60 = 1/15 }}} of a full circle
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The angle between the hand, in terms of a full hour is:
( minus the initial gap ) + ( how far the minute hand goes ) - ( minus how far the hour hand goes )
{{{ -1/12 + 4/5 -1/15 }}}
{{{ -5/60 + 48/60 - 4/60 }}}
{{{ 39/60 }}}
This is 49 minutes out of 60 minutes, or, in degrees:
{{{ ( 39*6 ) / 360 = 234/360 }}}
The answer is 234 degrees
You might want a 2nd opinion, too. I could
 *easily * have made a mistake