Final answer:
The synonym 'strait' fits in the first sentence, indicating a narrow body of water, while 'avenue' is the appropriate synonym in the second sentence, referring to a direct way of passing information, such as addressing a complaint.
Step-by-step explanation:
To answer the questions, we must select the synonym that best completes each sentence in context according to the provided definitions and synonyms of channel. For the first sentence, 'She was the first swimmer to cross the strait between the two countries,' the synonym strait fits as it refers to a narrow body of water between two land masses, which is typically what a swimmer would cross. In the second sentence, 'If you want your complaint to be addressed, you need to go through the appropriate avenue,' the best synonym for channel would be avenue because it suggests a direct path for a process or approach, in this case, to resolve a complaint.