Final answer:
Using properties of parallelograms, we find that neither the measure of ∠QRT nor ∠SQR is 72°. The answer is that the measure of ∠TRQ is 108°, since adjacent angles in a parallelogram add up to 180°.
Step-by-step explanation:
The question asks us to determine the truth of a statement involving angles in a parallelogram named QRT and a point S outside of it. If m∠QST is 72°, we must use the properties of parallelograms and the relationships between angles to find the correct answer.
In a parallelogram, opposite angles are equal. Therefore, since QRT is a parallelogram, ∠QRT equals ∠STQ. However, we do not have information on ∠STQ, and neither do we know the relationship between S and our parallelogram directly. Statement c) suggests that the measure of ∠QRT is 72°. If this were true, ∠STQ (which is the alternate interior angle formed when line ST crosses the parallel lines QT and RS) must also be 72° which would not be consistent since angle QST which is adjacent to STQ is given as 72°. It is not possible for ∠STQ and ∠QST to both be 72°, so option c) is incorrect.
Considering all options, the correct answer is e) the measure of ∠TRQ is 108°, as adjacent angles in a parallelogram add up to 180°. If ∠QST is 72°, then ∠STQ is also 72°, as it is part of the exterior angle of parallelogram QRT at vertex T. Therefore, to find ∠TRQ, we subtract the angle ∠STQ from 180° (180° - 72° = 108°), verifying that the measure of ∠TRQ must indeed be 108°.