Question

1. given the squarew xyz, wz = 17. determine the missing measures. zy = m∠wrz = wy = m∠xyz = rx = m∠zwy =

Explanation:

Step1: Find \(ZY\)

In a square, all sides are equal. Given \(WZ = 17\), so \(ZY=17\).

Step2: Find \(WY\)

Use the Pythagorean theorem for right - triangle \(WZY\) (since in square \(WXYZ\), \(\angle WZY = 90^{\circ}\)). If \(a=b = 17\) (sides of the square), and \(c\) is the diagonal \(WY\). Then \(c=\sqrt{a^{2}+b^{2}}=\sqrt{17^{2}+17^{2}}=\sqrt{2\times17^{2}} = 17\sqrt{2}\).

Step3: Find \(RX\)

The diagonals of a square bisect each other. So \(RX=\frac{WY}{2}\). Since \(WY = 17\sqrt{2}\), then \(RX=\frac{17\sqrt{2}}{2}\).

Step4: Find \(m\angle WRZ\)

The diagonals of a square are perpendicular to each other. So \(m\angle WRZ = 90^{\circ}\).

Step5: Find \(m\angle XYZ\)

Each interior angle of a square is \(90^{\circ}\). So \(m\angle XYZ=90^{\circ}\).

Step6: Find \(m\angle ZWY\)

The diagonals of a square bisect the vertex angles. The vertex angle of a square is \(90^{\circ}\), so \(m\angle ZWY=\frac{90^{\circ}}{2}=45^{\circ}\).

Answer:

\(ZY = 17\), \(WY=17\sqrt{2}\), \(RX=\frac{17\sqrt{2}}{2}\), \(m\angle WRZ = 90^{\circ}\), \(m\angle XYZ = 90^{\circ}\), \(m\angle ZWY=45^{\circ}\)