Question

look at this diagram: if $overleftrightarrow{oq}$ and $overleftrightarrow{rt}$ are parallel lines and $mangle qpn = 40^{circ}$, what is $mangle qps$?

Explanation:

Step1: Identify angle - relationship

$\angle QPN$ and $\angle QPS$ are supplementary angles since they form a linear - pair.

Step2: Use the supplementary - angle property

The sum of the measures of two supplementary angles is $180^{\circ}$. Let $m\angle QPN = 40^{\circ}$ and $m\angle QPS=x$. Then $m\angle QPN + m\angle QPS=180^{\circ}$, so $x + 40^{\circ}=180^{\circ}$.

Step3: Solve for the unknown angle

Subtract $40^{\circ}$ from both sides of the equation: $x=180^{\circ}-40^{\circ}=140^{\circ}$.

Answer:

$140$