The location for the measurement of the Indian Standard Time is 82.5 degrees East of the Prime Meridian. The Prime Meridian is a line of longitude that runs north-south and passes through Greenwich, London. It serves as the reference point for measuring longitude and is considered as 0 degrees.

In India, the Indian Standard Time is determined based on the 82.5 degrees East line of longitude. This means that Indian Standard Time is 5 hours and 30 minutes ahead of Coordinated Universal Time (UTC+5:30).

Option 1, 72.5 degrees East of the Prime Meridian, is not the correct location for the measurement of Indian Standard Time. Similarly, option 2, 77.5 degrees East of the Prime Meridian, and option 3, 80 degrees East of the Prime Meridian, are also incorrect.

Therefore, the correct answer is option 4, 82.5 degrees East of the Prime Meridian.