Question

look at this diagram: if np and qs are parallel lines and m∠qrt = 57°, what is m∠qro?

Explanation:

Step1: Identify angle - relationship

$\angle QRT$ and $\angle QRO$ are supplementary angles (linear - pair of angles).

Step2: Use the supplementary - angle property

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

Step3: Solve for $m\angle QRO$

Given $m\angle QRT = 57^{\circ}$, then $m\angle QRO=180^{\circ}-m\angle QRT$. Substitute $m\angle QRT = 57^{\circ}$ into the equation: $m\angle QRO = 180 - 57=123^{\circ}$.

Answer:

$123^{\circ}$