Question

figure wxyz is a parallelogram.
which angle measures are correct? choose three correct answers.
$m\angle z = 55^\circ$
$m\angle x = 55^\circ$
$m\angle w = 125^\circ$
$m\angle z = 125^\circ$
$m\angle w = 55^\circ$

Explanation:

Step1: Recall parallelogram angle rules

In a parallelogram, consecutive angles are supplementary ($m\angle A + m\angle B = 180^\circ$), and opposite angles are equal.

Step2: Find $\angle Z$

$\angle Z$ and $\angle Y$ are consecutive, so:
$m\angle Z = 180^\circ - 125^\circ = 55^\circ$

Step3: Find $\angle X$

$\angle X$ is opposite $\angle Z$, so:
$m\angle X = m\angle Z = 55^\circ$

Step4: Find $\angle W$

$\angle W$ is opposite $\angle Y$, so:
$m\angle W = m\angle Y = 125^\circ$

Answer:

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