The monomer of the polymer is (a)

We are interested to determine the monomer of the given polymer. On acid treatment, isobutene is converted into isobutyl carbonium ion .further deprotonation results in the two products (a) and (b). This product (a) and (b) undergoes the polymerization reaction and form a cationic intermediate which elongates the polymer chain. The reaction is terminated by the addition of a negatively charged Lewis base. This can be explained based on the following diagram, POLYMERS 28