A number divisible by 45 must be divisible by both 5 and 9.
For divisibility by 5, the last digit must be 0 or 5.
For divisibility by 9, the sum of digits must be divisible by 9. 7+6+9+x = 22+x. If x=5, 22+5=27, which is divisible by 9.
The missing digit is 5.