which angles are consecutive interior angles?
image of two parallel lines (np and qs) cut by a transversal (mt) with points o on np and r on qs. angles: ∠por and ∠qro; ∠por and ∠qrt; ∠por and ∠sro; ∠por and ∠srt (multiple choice options)

Question

Accepted Answer

# Explanation:
## Step1: Recall Consecutive Interior Angles Definition
Consecutive interior angles are two angles that lie between two lines (the parallel lines, here $NP$ and $QS$) and on the same side of the transversal (here $MT$). They are supplementary.

## Step2: Analyze Each Option
- **Option 1: $\angle POR$ and $\angle QRO$**
  $\angle POR$ is above $NP$, $\angle QRO$ is below $QS$ on the left of transversal? Wait, no: $NP \parallel QS$, transversal $MT$. $\angle POR$ is between $NP$ and the transversal (interior? Wait, $NP$ and $QS$ are the two lines. $\angle POR$ is at $O$ on $NP$, between $NP$ and transversal $MT$? Wait, no: $NP$ is horizontal, $MT$ is the transversal. $\angle POR$ is on the upper line $NP$, between $NP$ and the transversal? Wait, actually, consecutive interior angles must be between the two parallel lines ($NP$ and $QS$) and on the same side of the transversal. Let's check positions:
  - $\angle POR$: at $O$, between $NP$ (top line) and transversal $MT$, on the right side of transversal? Wait, $NP$ is from $N$ (left) to $P$ (right), $QS$ from $Q$ (left) to $S$ (right). Transversal $MT$ crosses $NP$ at $O$, $QS$ at $R$.
  - $\angle SRO$: at $R$, between $QS$ (bottom line) and transversal $MT$, on the same side (right) of transversal as $\angle POR$? Wait, no, let's re-express:
  Consecutive interior angles: between the two lines ($NP$ and $QS$) and same side of transversal. So $\angle POR$ is on $NP$, between $NP$ and $QS$? Wait, $NP$ is above $QS$, so the region between $NP$ and $QS$ is the interior. $\angle POR$ is at $O$, between $NP$ (top) and transversal $MT$, but actually, the two lines are $NP$ (top) and $QS$ (bottom), transversal $MT$. So $\angle POR$ is on $NP$, inside the "strip" between $NP$ and $QS$? Wait, no: $NP$ and $QS$ are parallel, transversal $MT$. So consecutive interior angles are both between $NP$ and $QS$ (interior) and same side of $MT$.

Let's check each angle:
  - $\angle POR$: at $O$, between $NP$ (top) and transversal $MT$, on the right side of $MT$ (since $P$ is right of $O$).
  - $\angle SRO$: at $R$, between $QS$ (bottom) and transversal $MT$, on the right side of $MT$ (since $S$ is right of $R$). So both are between $NP$ and $QS$ (interior) and same side (right) of transversal. Wait, no, let's visualize:

$NP$ is horizontal (left $N$, right $P$), $QS$ is horizontal (left $Q$, right $S$), transversal $MT$ goes from $M$ (top) through $O$ (on $NP$) to $R$ (on $QS$) to $T$ (bottom). So $\angle POR$ is the angle at $O$ between $PO$ (right along $NP$) and $OR$ (down along $MT$). $\angle SRO$ is the angle at $R$ between $SR$ (right along $QS$) and $RO$ (up along $MT$). Wait, no, maybe I mixed up. Let's recall: consecutive interior angles are same - side interior angles, formed when a transversal crosses two parallel lines. They are on the same side of the transversal and inside the two lines.

Let's check each option:
  - $\angle POR$ and $\angle QRO$: $\angle QRO$ is at $R$, between $QR$ (left along $QS$) and $RO$ (up along $MT$). So $\angle QRO$ is on the left side of transversal, $\angle POR$ on right? No, not same side.
  - $\angle POR$ and $\angle QRT$: $\angle QRT$ is at $R$, between $QR$ (left) and $RT$ (down). That's outside the two lines? No, not interior.
  - $\angle POR$ and $\angle SRO$: $\angle SRO$ is at $R$, between $SR$ (right) and $RO$ (up). So both $\angle POR$ (at $O$, between $PO$ (right) and $OR$ (down)) and $\angle SRO$ (at $R$, between $SR$ (right) and $RO$ (up)) are between the two lines ($NP$ and $QS$) and on the same side (right) of the transversal. Wait, but let's confirm the definition: consecutive interior angles are also called same - side interior angles, so they lie between the two lines and on the same side of the transversal. So $\angle POR$ is between $NP$ (top line) and $QS$ (bottom line)? Wait, $NP$ is above $QS$, so the area between them is the interior. $\angle POR$ is at $O$, between $NP$ and the transversal? No, $NP$ is a line, so the two lines are $NP$ and $QS$, transversal $MT$. So the interior is between $NP$ and $QS$. $\angle POR$ is on $NP$, so it's on the boundary, but in the context of the two lines, the interior angles are those between the two lines. Wait, maybe I made a mistake. Let's recall the exact definition: Consecutive interior angles are two angles that are on the same side of the transversal and inside (between) the two lines.

So line 1: $NP$, line 2: $QS$, transversal: $MT$.
  - $\angle POR$: on line $NP$, between $NP$ and $QS$ (since $NP$ is above $QS$, $\angle POR$ is below $NP$ and above $QS$? No, $NP$ and $QS$ are parallel, horizontal. So the region between them is the vertical strip between $NP$ (y - coordinate higher) and $QS$ (y - coordinate lower). $\angle POR$ is at $O$ (on $NP$), with one side along $NP$ (to the right, $PO$) and one side along $MT$ (down to $R$). So this angle is in the region between $NP$ and $QS$ (since $MT$ goes from $NP$ down to $QS$).
  - $\angle SRO$: at $R$ (on $QS$), with one side along $QS$ (to the right, $SR$) and one side along $MT$ (up to $O$). So this angle is also in the region between $NP$ and $QS$, and on the same side (right) of the transversal $MT$ (since both angles are on the right - hand side of $MT$ when looking at the transversal).

Wait, let's check other options:
  - $\angle POR$ and $\angle QRO$: $\angle QRO$ is at $R$, with one side along $QR$ (left) and one side along $RO$ (up). So this angle is on the left side of the transversal, so not same side.
  - $\angle POR$ and $\angle QRT$: $\angle QRT$ is at $R$, with one side along $QR$ (left) and one side along $RT$ (down). This angle is outside the two lines (below $QS$), so not interior.
  - $\angle POR$ and $\angle SRT$: $\angle SRT$ is at $R$, with one side along $SR$ (right) and one side along $RT$ (down). This angle is below $QS$, outside the two lines, so not interior.
  - $\angle POR$ and $\angle SRO$: $\angle SRO$ is at $R$, with one side along $SR$ (right) and one side along $RO$ (up). This angle is between $NP$ and $QS$ (interior) and same side (right) of transversal as $\angle POR$. So this should be the correct pair.

# Answer: $\angle POR$ and $\angle SRO$ (the option: $\boldsymbol{\angle POR}$ and $\boldsymbol{\angle SRO}$)

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QUESTION IMAGE

Question

Explanation:

Step1: Recall Consecutive Interior Angles Definition

Step2: Analyze Each Option

Answer: