Question

look at this diagram: if (overleftrightarrow{oq}) and (overleftrightarrow{rt}) are parallel lines and (mangle rsp = 136^{circ}), what is (mangle tsp)?

Explanation:

Step1: Recall linear - pair property

Linear - pair angles are supplementary, meaning their sum is 180°. $\angle RSP$ and $\angle TSP$ form a linear - pair.

Step2: Set up the equation

Let $m\angle TSP=x$. We know that $m\angle RSP + m\angle TSP=180^{\circ}$. Given $m\angle RSP = 136^{\circ}$, the equation is $136^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

$x=180^{\circ}-136^{\circ}$.
$x = 44^{\circ}$.

Answer:

$44^{\circ}$