To find a two-digit number less than 80 and greater than 65 that is divisible by both 2 and 9, we start by identifying numbers that meet these criteria.
- Divisibility by 2: The number must be even.
- Divisibility by 9: The number must be a multiple of 9.
The two-digit multiples of 9 in the range between 65 and 80 are:
- 72 (9 x 8)
- 81 (9 x 9, but this is greater than 80)
The only candidate in the specified range is 72. Additionally, 72 is even, satisfying the condition of being divisible by 2.
Therefore, the number you are looking for is 72.