Final answer:
The "extra" key has a value of "true", which is a Boolean data type in JSON, commonly used in REST APIs.
Step-by-step explanation:
The question asks to identify the data type of the value associated with the key "extra" in a REST API response, which is given as true. In JSON, which is commonly used for API responses, the boolean data type is used to represent true or false values. Therefore, the "extra" key has a value of the boolean data type.
The answer to the question is: The "extra" key value is a Boolean value.