Question

sqrt is a parallelogram. if ∠qst = 72°, which of the following statements is true? ∠sqr = 72° ∠qrt = 72° ∠qsr = 36° ∠trq = 108°

Explanation:

Step1: Recall property of parallelogram

In parallelogram SQRT, opposite - angles are equal and adjacent - angles are supplementary. Also, alternate - interior angles are equal for parallel sides. Since QS is a transversal for parallel sides QR and ST, $\angle QST$ and $\angle SQR$ are alternate - interior angles.

Step2: Apply angle - equality rule

Because QR$\parallel$ST and QS is a transversal, $\angle SQR=\angle QST$. Given $\angle QST = 72^{\circ}$, then $\angle SQR=72^{\circ}$.

Answer:

$\angle SQR = 72^{\circ}$