hi

i have small question why the angle in negative?

I know the s∠cos-1 (0.8) = s∠36.87

 

Is the key word "lagging"?

 

The definitions of 'lead' and 'lag' were decided by people. They had to choose whether to describe if the voltage was leading or the current was lagging, or the other way around. It's called a, "convention" which means nothing more than an agreement among people. Your job is to become familiar with the agreement so you can be understood when you communicate about power factors. That's all it is, a way of communicating effectively.