Question

question 10 (multiple choice worth 1 points)
(02.06rlc)
sqrt is a parallelogram. if \\( \angle qst = 72 ^ { \circ } \\), which of the following statements is true?
\\( \angle sqr = 72 ^ { \circ } \\)
\\( \angle qrt = 72 ^ { \circ } \\)
\\( \angle qsr = 36 ^ { \circ } \\)
\\( \angle trq = 108 ^ { \circ } \\)

Explanation:

Step1: Recall properties of parallelogram

In parallelogram \(SQRT\), \(SQ\parallel RT\) and \(QR\parallel ST\). Alternate - interior angles are equal when a transversal intersects parallel lines. The diagonals of a parallelogram bisect each other, but we use the property of parallel lines and transversals here.
Since \(SQ\parallel RT\) and \(QS\) is a transversal, \(\angle SQR\) and \(\angle QST\) are alternate - interior angles.

Step2: Apply alternate - interior angles property

For parallel lines \(SQ\parallel RT\) and transversal \(QS\), we have the formula for alternate - interior angles: \(\angle SQR=\angle QST\) (If \(a\parallel b\) and \(c\) is a transversal, then alternate - interior angles are equal). Given \(\angle QST = 72^{\circ}\), substituting into the formula \(\angle SQR=\angle QST\), we get \(\angle SQR = 72^{\circ}\).

Answer:

\(\angle SQR = 72^{\circ}\)