The payout is 35 to 1, not the odds. The odds are 37 or 38 to 1, depending on whether the wheel has a double zero along with a zero.
Actually reading is your friend.
You misunderstand the difference between odds and probabilities.
On a single zero wheel, the odds are 36 to 1; on a double-zero wheel, the odds are 37 to 1.
An odds of 36:1 means that you are 36 times as likely to lose, as you are to win. In other words, the probability of winning = 1 / (36 + 1) = 1 / 37.
The reason odds are used in preference to probabilities in gambling is that they translate directly into a payout (except in games, such as roulette where the house rigs the game to take their cut).