1 part its done: with IR peaks you can predict its molecular structure (funcional groups, if you have got molecular formula is a great help) and then with polymarisation degree you can find molecular weight
Lamis Saleh polymerisation degree you can search tables and index from internet or books. Like you don't have molecular formula, only IR can predict the monomer with peaks (e.g. between 2800-3200 nm it's OH group). i hope i could help you