Question

In quadrilateral PQRS, m∠RQS = 25° and PS = QR. What measure of ∠PSQ would confirm that PQRS is a parallelogram?

m∠PSQ = [ ]°

Answer 1

25°

Explanation:

If sides PS and QR are parallel, then ∠PSQ and ∠RQS are alternate interior angles, hence congruent. That is, ∠PSQ ≅ ∠RQS = 25°.

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Comment on the problem statement

Confirming that two sides are parallel does not confirm the figure as a parallelogram. It could be a trapezoid. The given condition is necessary, but is not sufficient to do the confirmation.