Final answer:
The correct answer to describe a pleasant desert climate is 'balmy', which is option (C). The term signifies warm and pleasant weather, suitable to depict a fair day for pyramid workers.
Step-by-step explanation:
The question provided involves vocabulary, asking for the correct adjective to describe the climate of the desert in which pyramid workers might have enjoyed a fair day. The correct answer here is (C) balmy which means pleasantly warm weather. The other options do not accurately describe a type of weather. Vigilant (A) means keeping careful watch for possible danger or difficulties; invincible (B) means too powerful to be defeated or overcome; facsimile (D) means an exact copy, especially of written or printed material; and archaic (E) means very old or old-fashioned.