Question

1. m∠xwy=______ m∠yxz=____ m∠wvz=____ m∠xwz=____ m∠xzy=______

Explanation:

Step1: Find \(m\angle XWY\)

Since \(WXYZ\) is a rectangle, the diagonals \(WZ\) and \(XY\) are equal and bisect each other. \(\triangle WXY\) is isosceles. \(\angle XWY=\angle WXY\). Using the property that the sum of angles in a triangle is \(180^{\circ}\), and \(\angle WVX = 64^{\circ}\), then \(\angle XWY=\frac{180 - 64}{2}=58^{\circ}\)

Step2: Find \(m\angle YXZ\)

\(\angle YXZ\) and \(\angle XWY\) are alternate - interior angles (because \(WX\parallel YZ\) and \(WY\) is a transversal). So \(m\angle YXZ = 26^{\circ}\) (since \(90 - 64=26\))

Step3: Find \(m\angle WVZ\)

\(\angle WVZ\) and \(\angle XVW\) are supplementary. So \(m\angle WVZ=180 - 64 = 116^{\circ}\)

Step4: Find \(m\angle XWZ\)

\(\angle XWZ\) is a right - angle in the rectangle \(WXYZ\), so \(m\angle XWZ = 90^{\circ}\)

Step5: Find \(m\angle XZY\)

\(\angle XZY=\angle YXZ\) (alternate - interior angles as \(WX\parallel YZ\) and \(XZ\) is a transversal). So \(m\angle XZY = 26^{\circ}\)

Answer:

\(m\angle XWY = 58^{\circ}\)
\(m\angle YXZ = 26^{\circ}\)
\(m\angle WVZ = 116^{\circ}\)
\(m\angle XWZ = 90^{\circ}\)
\(m\angle XZY = 26^{\circ}\)