Question

figure wxyz is a parallelogram.
which angle measures are correct? select three options.
□ ( mangle x = 55^circ )
□ ( mangle w = 125^circ )
□ ( mangle w = 55^circ )
□ ( mangle z = 125^circ )
□ ( mangle z = 55^circ )

Explanation:

Step1: Recall properties of parallelograms

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

Step2: Analyze angle \(Y = 125^\circ\)

• Angle \(X\) and angle \(Y\) are consecutive angles, so \(m\angle X=180^\circ - 125^\circ = 55^\circ\).
• Angle \(W\) is opposite to angle \(Y\), so \(m\angle W = 125^\circ\).
• Angle \(Z\) is opposite to angle \(X\), so \(m\angle Z=55^\circ\). Also, angle \(Z\) and angle \(Y\) are consecutive, so \(m\angle Z = 180^\circ - 125^\circ = 55^\circ\) (confirming). And angle \(W\) and angle \(X\) are consecutive, \(m\angle W=180^\circ - 55^\circ = 125^\circ\) (confirming).
• Check each option:
• \(m\angle X = 55^\circ\): Correct (from consecutive angles with \(Y\)).
• \(m\angle W = 125^\circ\): Correct (opposite to \(Y\)).
• \(m\angle W = 55^\circ\): Incorrect (opposite to \(Y = 125^\circ\), so should be \(125^\circ\)).
• \(m\angle Z = 125^\circ\): Incorrect (opposite to \(X = 55^\circ\), so should be \(55^\circ\)).
• \(m\angle Z = 55^\circ\): Correct (opposite to \(X\) or consecutive to \(Y\)).

Answer:

The correct options are:

• \(m\angle X = 55^\circ\)
• \(m\angle W = 125^\circ\)
• \(m\angle Z = 55^\circ\)