why does each time zone extend 7 1/2 degrees oneach side of central meridian rather than extending from 0 degrees to 15 degree?
I don't understand what you're trying to ask.
The reason each time zone extends 7 1/2 degrees on each side of the central meridian, instead of extending from 0 degrees to 15 degrees, is because the Earth is divided into 24 time zones to represent the 24 hours in a day.
The Earth rotates 360 degrees in 24 hours, which means it rotates 15 degrees per hour. By dividing the Earth into 24 time zones, each time zone represents one hour of time.
However, due to historical and practical reasons, the time zones are not perfectly 15 degrees wide. Instead, they are slightly narrower and vary in width. This is because time zones are designed to align more closely with political boundaries and other regional considerations.
To determine the actual width of each time zone, you need to divide the 360 degrees of the Earth's circumference by 24, which gives you 15 degrees. Then, since each time zone extends on both sides of the central meridian, you divide 15 degrees by 2 to get 7 1/2 degrees. This means that each time zone extends 7 1/2 degrees to the east and 7 1/2 degrees to the west of the central meridian.
So, the reason for the specific width of each time zone, extending 7 1/2 degrees on each side of the central meridian, is a result of the need to represent 24 hours of time while also considering practical and regional factors.