Question

look at this diagram: if $overleftrightarrow{oq}$ and $overleftrightarrow{rt}$ are parallel lines and $mangle{opn}=121^{circ}$, what is $mangle{ops}$?

Explanation:

Step1: Identify angle - relationship

$\angle OPN$ and $\angle OPS$ are supplementary angles (linear - pair of angles).

Step2: Use the supplementary - angle property

The sum of supplementary angles is $180^{\circ}$. So, $m\angle OPN+m\angle OPS = 180^{\circ}$.

Step3: Solve for $m\angle OPS$

Given $m\angle OPN = 121^{\circ}$, then $m\angle OPS=180^{\circ}-m\angle OPN$. Substitute $m\angle OPN = 121^{\circ}$ into the equation: $m\angle OPS = 180 - 121=59^{\circ}$.

Answer:

$59$