Question

1. what is m∠z?

Explanation:

Step1: Recall sum of angles in a quadrilateral

The sum of the interior angles of a quadrilateral is $360^{\circ}$.

Step2: Set up angle - sum equation

Let $m\angle Z=x$. We know that $m\angle W = 80^{\circ}$, $m\angle X$ is unknown, $m\angle Y=120^{\circ}$, and we want to find $x$. Using the angle - sum formula for a quadrilateral $m\angle W+m\angle X+m\angle Y + m\angle Z=360^{\circ}$.

Step3: Substitute known values

$80^{\circ}+m\angle X + 120^{\circ}+x=360^{\circ}$. Since we don't need to find $m\angle X$ explicitly, we can also use the fact that we can directly sum the known angles and subtract from $360^{\circ}$. The sum of the known angles is $80^{\circ}+120^{\circ}=200^{\circ}$.

Step4: Solve for $m\angle Z$

$m\angle Z=360^{\circ}-(80^{\circ}+120^{\circ})$.
$m\angle Z = 360^{\circ}-200^{\circ}=160^{\circ}$.

Answer:

$160^{\circ}$