$\alpha$ -Terpinene, $\mathrm{C}_{10} \mathrm{H}_{16}$, is a pleasant-smelling hydrocarbon that has been isolated from oil of marjoram. On hydrogenation over a palladium catalyst, $\alpha$ -terpinene reacts with 2 molar equivalents of $\mathrm{H}_{2}$ to yield a hydrocarbon, $\mathrm{C}_{10} \mathrm{H}_{20}$. On ozonolysis, followed by reduction with zinc and acetic acid, $\alpha$ -terpinene yields two products, glyoxal and 6 -methylheptane- 2,5 -dione.
(a) How many degrees of unsaturation does $\alpha$ -terpinene have?
(b) How many double bonds and how many rings does it have?
(c) Propose a structure for $\alpha$ -terpinene.