Question

which angles are consecutive interior angles? image of two parallel lines (rt and oq) cut by a transversal (un) with points r, s, t on one line and o, p, q on the other, and u, s, p, n on the transversal options: ∠rsp and ∠rsu; ∠rsp and ∠qpn; ∠rsp and ∠tsu; ∠rsp and ∠ops

Explanation:

Step1: Recall Consecutive Interior Angles

Consecutive interior angles are formed when a transversal crosses two parallel (or non - parallel) lines. They lie between the two lines and on the same side of the transversal.

Step2: Analyze Each Option

• Option 1: $\angle RSP$ and $\angle RSU$: These angles are not between two lines cut by a transversal in the consecutive interior angle way. $\angle RSU$ is on the same line as the transversal and not between two lines.
• Option 2: $\angle RSP$ and $\angle QPN$: $\angle QPN$ is not between the two lines ( $RT$ and $OQ$) cut by the transversal $UN$.
• Option 3: $\angle RSP$ and $\angle TSU$: These are vertical angles - like angles, not consecutive interior angles.
• Option 4: $\angle RSP$ and $\angle OPS$: The lines $RT$ and $OQ$ are cut by the transversal $UN$. $\angle RSP$ and $\angle OPS$ lie between $RT$ and $OQ$ and on the same side of the transversal $UN$, so they are consecutive interior angles.

Answer:

$\angle RSP$ and $\angle OPS$