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 = $ $\boldsymbol{\text{dropdown}}$ because they are $\boldsymbol{\text{dropdown}}$

answer
attempt 1 out of 2
you must answer all questions above in

Explanation:

Step1: Recall triangle angle sum

The sum of angles in $\triangle OPQ$ is $180^\circ$.

Step2: Calculate $\angle POQ$

$\angle POQ = 180^\circ - 53^\circ - 59^\circ = 68^\circ$

Step3: Relate to parallel lines

Since $\overleftrightarrow{ROS} \parallel \overline{PQ}$, $\angle OPQ$ and the corresponding angle on line $\overleftrightarrow{ROS}$ at $O$ are equal, but first confirm $\angle OPQ$ is given as $59^\circ$, which is an alternate interior angle with the angle formed by $\overleftrightarrow{ROS}$ and $\overline{OP}$.

Answer:

$\text{m}\angle OPQ = 59^\circ$ because they are alternate interior angles