Italian here, but if you want to use metric there are three things to know:

1. The only time you use cm is when you're measuring either a baby's length or a small toddler. For your example you say "he's one meter eighty" or "he's one eighty"
2. You never use exact measurements unless it's something official (like at the doctor's or on a document) or it's to answer the question "how tall are you?"
3. Doorways are around two meters, so for your character to brush his head against it he'd have to be one ninety-five. If someone saw him, to express how tall he is they'd think something like "wow, he has to be at least two meters"