Expressions are derived for the relationship between the measured linewidths in angle-resolved valence-band photoemission spectra and the lifetimes of the photoelectron and photohole. The expressions are different for the energy-distribution curve (EDC), constant initial-state spectrum (CIS), and constant final-state spectrum modes of data acquisition, and are significantly angle dependent for the EDC and CIS. The circumstances in which the lifetime widths of the photoelectron and photohole can be separated from each other are discussed with special reference to a debate on high-temperature superconductors. Surface states offer the only case where the photohole lifetime can be rigorously isolated. The nearly-free-electron approximation is elaborated and used to explain some counterintuitive behavior in recent data on Ag(100).