Question

∠4 + ∠1 = 180°
is m || n? choose your answer...
how do you know? choose your answer...

Explanation:

Step1: Vertical angles property

Since $\angle 2$ and $\angle 1$ are vertical angles, $\angle 2=\angle 1$.

Step2: Consecutive interior angles

Given $\angle 4+\angle 1 = 180^{\circ}$, substituting $\angle 2$ for $\angle 1$ gives $\angle 4+\angle 2=180^{\circ}$.

Step3: Parallel line criterion

If consecutive interior angles ($\angle 4$ and $\angle 2$) are supplementary, then the lines $m$ and $n$ are parallel.

Answer:

Yes, \(m\parallel n\) because \(\angle 4+\angle 2 = 180^{\circ}\) (consecutive interior angles are supplementary).