Evidently a " transmission line" is not the wire that send your audio signal to the transmitter.
So, what is it?
A transmission line carries the RF from the transmitter to the antenna, but is not part of the antenna. There are two types that I know of: unbalanced and balanced. An unbalanced transmission line is a shielded cable with the RF on the center conductor just like a video cable. For high power the transmission line may be a copper pipe with an inner conductor designed to carry many watts. A balanced transmission line is just like 300-ohm ribbon cable, unshielded, but with each conductor 180-degrees out of phase with the other so that minimal signal leakage occurs on its path.
Under part 15 the "transmission line" is counted as part of the total length together with the antenna and ground lead, perhaps because many amateurs will use an un-shielded, unbalanced transmission line which will certainly radiate, and is technically the wrong way to do things.
Coaxial cable may or may not radiate. It depends on if the RF current in the center conductor balances out the RF current in the shield. Sometimes a shorted quarter-wave coaxial stub is actually used as an antenna. This is called the "folded monopole," and it is often used for licensed AM stations. So, don't let anyone tell you that coax doesn't radiate.
And that's why so many use a "common mode" balun on the coax at the antenna to prevent the coax shield from skewing the radiated pattern due to RF on the shield.