Question

look at this diagram: if $overleftrightarrow{oq}$ and $overleftrightarrow{rt}$ are parallel lines and $mangle tsp = 111^{circ}$, what is $mangle ops?

□^{circ}$

Explanation:

Step1: Identify angle - relationship

$\angle TSP$ and $\angle OPS$ are supplementary angles since $\overleftrightarrow{OQ}$ and $\overleftrightarrow{RT}$ are parallel lines and $\overleftrightarrow{UN}$ is a transversal.

Step2: Use the supplementary - angle formula

The sum of supplementary angles is $180^{\circ}$. Let $m\angle TSP = 111^{\circ}$ and $m\angle OPS=x$. Then $x + 111^{\circ}=180^{\circ}$.

Step3: Solve for $x$

$x=180^{\circ}- 111^{\circ}=69^{\circ}$.

Answer:

$69$