Whats the relation between degree and time, is there any historical answer.
A degree can be broken into even smaller measurements, much like a foot can be broken down into inches, and say, centimeters. One practical reason we break a degree into even smaller parts is so we can accurately measure the nautical space between distant objects in deep space. I don't have a specific example, but consider the following:
The sun is roughly 92.95 million miles away from Earth. Now think of when you look into a night sky and see stars. The nearest star is 4.32 light years (2.5396X10^13 miles) away from earth. If you wanted to figure out the distance between the nearest star and a star nearby it, you would have to measure the angle in more precise units (minutes and seconds). This is because even an angle as small as 0degrees,0minutes, and 30seconds has a big arc length when the two objects at the end are, for instance, the distance from the earth to two distance stars.
If you don't understand what I'm saying then try this. Find two distant objects (the farther from you the better) (trees, buildings, ext.).Make an angle with your pointer finger and your index finger and line the tips of your fingers up with these two distant objects. Notice that although the angle between your fingers is rather small, the distance between the two distant objects is rather big. Now imagine keeping your fingers fixed on these objects and walking backwards. The distance between the two objects stays fixed, but as you get farther and farther away from the objects, the angle your fingers make will get smaller, and smaller.
In short, we need smaller units of angle measures (other than a degree) so we can more accurately measure distant objects.
Lastly, there is a relation between angles measured in degree, minutes, and seconds and time.
Circular motion, and rotation create angles. Its not a coincidence that there are roughly 360 days in a year, and 360 degrees in a full rotation. This means that as the Earth orbits the Sun, every day, the Earth travels through about one degree of its orbit. There is a relation between time and our position around the sun (hence why our calendar has named seasons, Although the seasons we experience are due to both our position around the sun and because of Earth's axis being tilt).
One degree is 60minutes. 60 minutes is 3600seconds. This statement holds true for measurements of time as well. I'm not sure who first came up with the concept of angular measurements, but I'm willing to bet its a very old astronomer.