Final answer:
Without context on how angles 4, 5, and UPS are related, we cannot determine the expression for the measure of angle UPS.
Step-by-step explanation:
The student has provided two expressions for the measures of angles 4 and 5, m∠4 = (3x + 7) degrees and m∠5 = (9x - 43) degrees, and is seeking the measure of angle UPS. Without additional context it's unclear how angles 4, 5, and UPS are related. Generally, if angles are supplementary, their measures sum to 180 degrees; if they're complementary, their sum is 90 degrees; if they're adjacent angles on a line, they sum to 180 degrees; and if they're vertical angles, they are congruent.
Assuming angle UPS relates to the given angles 4 and 5, we would need specific information on that relationship to find an accurate expression for m∠UPS. As no such information is provided, and since none of the reference information seems relevant to this particular problem, we cannot determine a correct expression for m∠UPS from the given options.