The given question is a sentence completion task, where we have to select the appropriate verb to complete the sentence: "Director, he said, would ....... the matter at once." Let's analyze each provided option:
- Invigilate: This verb means to supervise students during an examination. It is not suitable for the context, as the sentence does not pertain to an examination scenario.
- Explore: To explore means to travel through an area or to look into something systematically. While it is somewhat related to examining aspects of a matter, it does not imply a detailed and thorough examination, as required by the context.
- Investigate: This verb means to carry out a systematic or formal inquiry to discover and examine the facts. This is the most appropriate choice, as it implies a thorough examination of the details, which is suitable for the context of the sentence where a director would need to address a matter promptly and comprehensively.
- Survey: This means to look at or examine all parts of something carefully. While similar in meaning, "survey" pertains to overviewing without necessarily indicating a thorough inquiry into details, unlike "investigate."
Based on the meanings and context given, the correct choice is "investigate". This verb best fits the context of the sentence where a director is expected to examine and gather facts about a matter immediately.
Therefore, the complete sentence should read: "Director, he said, would investigate the matter at once."