A right angle on a clock occurs when the hour and minute hands form an angle of 90 degrees. This happens twice every hour.

Steps to calculate:

1. Total Time Range: The time interval from 11 PM to 2 PM is 15 hours (from 11 PM to 12 AM is 1 hour, then 12 AM to 2 PM is 14 hours).

2. Right Angles per Hour: In every hour, two right angles are formed by the clock's hands.

3. Total Right Angles: In 15 hours, the total number of right angles formed is: $2 \times 15 = 30$

Thus, the number of right angles formed from 11 PM to 2 PM is 30.

Would you like further explanation or any details about the reasoning?

Here are five related questions you might find interesting:

1. How many times do the hour and minute hands overlap in a 12-hour period?
2. What is the total number of right angles formed in a full day (24 hours)?
3. At what exact times between 1 PM and 2 PM do the clock hands form right angles?
4. How would the calculation change if we wanted to count obtuse angles instead of right angles?
5. Can the clock hands ever form an acute angle between 11 PM and 2 PM?

Tip: Remember, in a clock, the hands form the same angle twice every hour (once going forward and once backward).