The time is 7:05:27 (and .27 seconds)
Calculating by degree
Assume the minute hand doesn't move in steps ... it just glides continuously and analogly, at the rate of 6 degrees per minute. At 'M' minutes past the hour, it's pointing toward an azimuth of 6M degrees.
Assume the hour hand doesn't move in steps either; it also glides in a smooth analog fashion, at the rate of 30 degrees per hour. At 'M' minutes past 7:00, the hour hand points toward an azimuth of 210 + 30(M/60) = 210 + M/2 degrees. The direction opposite the hour hand is 180 degrees different, or 30 + M/2.
That's the direction we want the minute hand pointing.
6M = 30 + M/2
12M = 60 + M
11M = 60
M = 60/11 minutes = 5 minutes 27.27 seconds after 7:00.
Using this formula
The formula M = H * (60/11) gives the whole and decimal minutes past the hour for times that have overlapping hour and minute hands, where H is an hour between 1 and 10. Adding 6 hours to these times will provide the opposite times, except for 6 o'clock exactly (from 0:00:00).
270 degrees
get yourself a cartesian circle, or just look at one online and translate it from there 3,6,9, and 12 would all be 90 deg increments.
obtuse
It is a obtuse angle.
12 and 6
30 degrees
270 degrees
120 degrees and 240 degrees.
get yourself a cartesian circle, or just look at one online and translate it from there 3,6,9, and 12 would all be 90 deg increments.
At 3 hours 45 minutes there is not an acute angle between the hands of the clock (unless you extend the hands backwards).
1 o'clock 2 o'clock 3 oclock.............9 o'clock 10 o'clock 11 o'clock 12 o'clock
30 degrees.
60o
150
obtuse
It is a obtuse angle.
12 and 6