Question

in the figure below, $\triangle opq$ is drawn. the line $\overleftrightarrow{ros}$ is drawn such that $\overleftrightarrow{ros} \parallel \overline{pq}$.

$\text{m}\angle opq = \text{m}\angle por$ because they are alternate interior angles.

$\text{m}\angle pqo = \quad$ because they are

Explanation:

Since $\overleftrightarrow{ROS} \parallel \overline{PQ}$, the angle corresponding to $\angle PQO$ is $\angle QOS$ (which is $x^\circ$). These two angles are alternate interior angles formed by the transversal $\overline{OQ}$ cutting the parallel lines $\overleftrightarrow{ROS}$ and $\overline{PQ}$.

Answer:

$\boldsymbol{m\angle PQO = m\angle QOS}$ because they are alternate interior angles