Question

look at this diagram: if $overleftrightarrow{np}$ and $overleftrightarrow{qs}$ are parallel lines and $mangle por = 120^{circ}$, what is $mangle qro$?

Explanation:

Step1: Identify angle - relationship

$\angle POR$ and $\angle QRO$ are same - side interior angles.

Step2: Recall property of same - side interior angles

Same - side interior angles formed by two parallel lines and a transversal are supplementary, i.e., their sum is $180^{\circ}$.
Let $m\angle QRO=x$. We know that $m\angle POR = 120^{\circ}$, and $x + 120^{\circ}=180^{\circ}$.

Step3: Solve for $x$

$x=180^{\circ}- 120^{\circ}$
$x = 60^{\circ}$

Answer:

$60$