Question

look at this diagram: if mo and pr are parallel lines and m∠onq = 125°, what is m∠pqs?

Explanation:

Step1: Identify vertical - angle relationship

$\angle ONQ$ and $\angle PQR$ are vertical angles. So, $m\angle PQR=m\angle ONQ = 125^{\circ}$.

Step2: Use linear - pair property

$\angle PQR$ and $\angle PQS$ form a linear - pair. Since the sum of angles in a linear - pair is $180^{\circ}$, we have $m\angle PQR + m\angle PQS=180^{\circ}$.

Step3: Solve for $m\angle PQS$

$m\angle PQS=180^{\circ}-m\angle PQR$. Substitute $m\angle PQR = 125^{\circ}$ into the equation, then $m\angle PQS=180 - 125=55^{\circ}$.

Answer:

$55$