After 12:00, when are the hands of the clock at 180 degree to each other for the first time?

Every hour the minute hand of the clock moves one full circle or
360 degree. During the same period the hour hand moves by 1/12th of a complete circle, or 30
degrees.

Thus every 1 hour after 12:00 the net angle between the
hour hand and minute hand increases by:

360 - 30 = 330
degrees

Therefore:

The time taken for
the angle between hour and minute hand to increase from by 180 degrees from 0 to 180 degrees is
given by:

Time for the angle to increase by 180 degrees =
180*(1/330)

= 6/11 hours.

= (6/11)*60 =
32.7272 minutes = 32 minutes and 44
seconds

Therefore:

Time after 12:00
when hands of clock are at 180 degrees to each others = 12:32:44