Question

look at this diagram: if oq and rt are parallel lines and m∠opn = 110°, what is m∠ops?

Explanation:

Step1: Identify angle - relationship

$\angle{OPN}$ and $\angle{OPS}$ are supplementary angles (linear - pair).

Step2: Use supplementary - angle formula

The sum of supplementary angles is $180^{\circ}$. Let $m\angle{OPS}=x$. Then $m\angle{OPN}+x = 180^{\circ}$. Given $m\angle{OPN}=110^{\circ}$, we have $110^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

$x=180^{\circ}-110^{\circ}=70^{\circ}$.

Answer:

$70$