Question

"a router interface has been assigned an ip address of 172.16.192.166 with a mask of 255.255.255.252. to which subnet does the ip address belong?"

Answer 1

An interface with an address of 172.16.192.166/30 has only 2 hosts per subnet. 172.16.192.166 and 172.168.192.169 are those hosts.
This configuration is usually only assigned to serial links with one source and one destination address like a T1/3.