How to say it when you can't be present due to some reason

Question

In Western countries, can you call your teacher or boss to tell them that you'll be absent due to some reason; for example, you need to take care of your sick child, or you need to attend a very important wedding, or you need to fix an emergency at home: your water pipe is broken.

If yes, what do you name this act?

Is there a similar phrase like "call in sick"?

Boss said to an employee: You've (xxx) three times in the last month.

Answer 1

In the U.S., the employee is often said to be taking a "personal day". The boss would say, "You've taken three personal days in the last month." Different workplaces might use different terms ("personal leave", etc.).