How many total episodes does the U.S. version of The Office have?

How to get close to this number

Multiply seasons by network season length. Nine seasons at roughly twenty-two episodes each gives around two hundred, which is the answer. The same arithmetic answers every American network show on this site, and the per-season constant is the only thing worth memorising.

The lead actor detail is the structurally interesting one: the central character left partway through the seventh season, and the show continued for two more without him. Very few series survive losing their lead, and the ones that do tend to be ensembles where the premise is a workplace rather than a person.

That is the same durability principle as the Doctor Who question on this site, from a different angle. A show built around a role can replace the actor; a show built around a setting can lose the character entirely. A show built around one specific person cannot do either, which is why premise design determines how long a series can possibly run.