So ∠ AOM+∠ AON =1/2 (∠ AOC+∠ AOB) = 90; ①

Because ∠ mon = ∠ aom-∠ aon = 40, ②

So according to ① and ②, ∠ AOM = 65 and ∠ AON = 25 can be calculated;

And because OM and ON are bisectors of ∠AOC and ∠AOB respectively,

So ∠ AOC = 2 * ∠ AOM = 130, ∠ AOB = 2 * ∠ AON = 50.