Question

8.$mangle s=$$mangle r=$$qr=$$qp=$

Explanation:

Step1: Identify parallelogram properties

In parallelogram \(QPRS\), opposite sides are equal, and consecutive angles are supplementary (sum to \(180^\circ\)).

Step2: Find length of \(QP\)

Opposite sides \(QP = RS\). Given \(RS = 14\), so \(QP = 14\).

Step3: Find length of \(QR\)

Opposite sides \(QR = SP\). Given \(SP = 8\), so \(QR = 8\).

Step4: Find \(m\angle R\)

Consecutive angles \(\angle Q + \angle R = 180^\circ\). Given \(m\angle Q = 105^\circ\), so:
\(m\angle R = 180^\circ - 105^\circ = 75^\circ\)

Step5: Find \(m\angle S\)

Opposite angles in parallelogram are equal, so \(m\angle S = m\angle Q = 105^\circ\).

Answer:

\(m\angle S = 105^\circ\)
\(m\angle R = 75^\circ\)
\(QR = 8\)
\(QP = 14\)