If $72\ast 72$ is divisible by 9, the missing $\ast$ digit will be:

According to the divisibility rule for 9, the sum of digits of the number must be a multiple of 9.Sum of given digits = $7+2+\ast +7+2=18+\ast$ For $(18+\ast )$ to be divisible by 9, the digit $\ast$ can be either 0 or 9 (since $18+0=18$ and $18+9=27$, both of which are divisible by 9).Therefore, the missing digit can be 0 or 9.