Question

select all the pairs of alternate interior angles. ∠poq and ∠pol ∠nol and ∠noq ∠klo and ∠pol ∠klo and ∠noq

Explanation:

Step1: Recall Alternate Interior Angles Definition

Alternate interior angles are formed when a transversal crosses two parallel lines. They lie between the two lines (interior) and on opposite sides of the transversal.

Step2: Analyze Each Pair

• $\angle POQ$ and $\angle POL$: These are adjacent angles, not alternate interior (no two parallel lines here as a transversal for them).
• $\angle NOL$ and $\angle NOQ$: Adjacent angles, not alternate interior.
• $\angle KLO$ and $\angle POL$: Let's check lines. If $KL$ and $OP$ are parallel (or the relevant lines), $\angle KLO$ (interior, left of transversal $LO$) and $\angle POL$ (interior, right of transversal $LO$) are alternate interior.
• $\angle KLO$ and $\angle NOQ$: $\angle KLO$ and $\angle NOQ$: If $KL \parallel OP$ and transversal $JQ$, $\angle KLO$ (interior, left) and $\angle NOQ$ (interior, right) are alternate interior. Wait, but first, correct pairs: Alternate interior angles require two parallel lines cut by a transversal. Assuming $KL \parallel NP$ (or similar) and transversal $JQ$, $\angle KLO$ (at $L$) and $\angle POL$ (at $O$) are between the lines, opposite sides of transversal. Also, $\angle KLO$ and $\angle NOQ$: Wait, maybe the correct pairs are $\boldsymbol{\angle KLO}$ and $\boldsymbol{\angle POL}$, and $\boldsymbol{\angle KLO}$ and $\boldsymbol{\angle NOQ}$? Wait, no—let's re-express.

Wait, the original options: Let's re-express the correct alternate interior pairs. When two lines (say $KL$ and $NP$) are cut by transversal $JQ$, the alternate interior angles are:

• $\angle KLO$ (at $L$, between $KL$ and $NP$, left of $JQ$) and $\angle NOQ$ (at $O$, between $KL$ and $NP$, right of $JQ$) – alternate interior.
• $\angle KLO$ (at $L$) and $\angle POL$ (at $O$) – wait, no, $\angle POL$ is at $O$, between $KL$ and $NP$? Wait, maybe the correct pairs are $\angle KLO$ and $\angle POL$, and $\angle KLO$ and $\angle NOQ$? Wait, the initial check marks might be wrong. Wait, no—let's re-define:

Alternate interior angles: two angles that lie between the two lines (interior), on opposite sides of the transversal, and are congruent if lines are parallel.

So, for transversal $JQ$ cutting lines $KL$ and $NP$ (assuming $KL \parallel NP$):

• $\angle KLO$ (interior, left of $JQ$) and $\angle NOQ$ (interior, right of $JQ$) – alternate interior.
• $\angle KLO$ (interior, left) and $\angle POL$ (interior, right) – wait, $\angle POL$ is at $O$, between $KL$ and $NP$? If $KL \parallel MP$ (or $NP$), then $\angle KLO$ (at $L$) and $\angle POL$ (at $O$) are between the lines, opposite sides of transversal $JQ$? Wait, maybe the correct pairs are $\boldsymbol{\angle KLO}$ and $\boldsymbol{\angle POL}$, and $\boldsymbol{\angle KLO}$ and $\boldsymbol{\angle NOQ}$? But the initial options with check marks: let's re-express.

Wait, the problem is to select all pairs. Let's correct:

• $\angle POQ$ and $\angle POL$: Adjacent (share a side), not alternate interior.
• $\angle NOL$ and $\angle NOQ$: Adjacent, not alternate interior.
• $\angle KLO$ and $\angle POL$: Alternate interior (between two lines, opposite sides of transversal).
• $\angle KLO$ and $\angle NOQ$: Alternate interior (between two lines, opposite sides of transversal).

Answer:

The correct pairs of alternate interior angles are $\boldsymbol{\angle KLO}$ and $\boldsymbol{\angle POL}$, and $\boldsymbol{\angle KLO}$ and $\boldsymbol{\angle NOQ}$. (So the options with check marks for $\angle KLO$ and $\angle POL$, and $\angle KLO$ and $\angle NOQ$ are correct; the other two are adjacent, not alternate interior.)