Question

look at this diagram: if \\(\overleftrightarrow{oq}\\) and \\(\overleftrightarrow{rt}\\) are parallel lines and \\(m\angle opn = 58^\circ\\), what is \\(m\angle rsu\\)? \\(\square^\circ\\)

Explanation:

Step1: Identify vertical angle

$\angle OPN$ and $\angle QPS$ are vertical angles, so $m\angle QPS = m\angle OPN = 58^\circ$.

Step2: Use parallel lines property

Since $\overleftrightarrow{OQ} \parallel \overleftrightarrow{RT}$, $\angle QPS$ and $\angle RSU$ are corresponding angles, so $m\angle RSU = m\angle QPS$.

Step1: Identify supplementary angle

$\angle OPN$ and $\angle QPU$ are supplementary? No, correct step: $\angle OPN$ and $\angle QPS$ are vertical angles, so $m\angle QPS=58^\circ$. Then $\angle QPS$ and $\angle RSU$ are same-side interior angles? No, $\angle RSU$ and $\angle QPS$: $\angle RSP$ is corresponding to $\angle OPN=58^\circ$, so $\angle RSU$ is supplementary to $\angle RSP$.

Step1: Find corresponding angle

$\angle OPN$ and $\angle RSP$ are corresponding angles, so $m\angle RSP = 58^\circ$.

Step2: Calculate supplementary angle

$\angle RSP$ and $\angle RSU$ are supplementary, so $m\angle RSU = 180^\circ - 58^\circ$.

Answer:

$122^\circ$

Wait, correction: