Question

which pair of angles are same - side interior angles?
∠5 and ∠4
∠6 and ∠4
∠5 and ∠1
∠8 and ∠2

Explanation:

Step1: Recall the definition of same - side interior angles

Same - side interior angles are two angles that lie between two lines and on the same side of a transversal.

Step2: Analyze each option

• For $\angle5$ and $\angle4$:

$\angle5$ lies between line $l$ and line $m$, and $\angle4$ lies between line $l$ and the transversal $t$. They are not in the correct position for same - side interior angles.

• For $\angle6$ and $\angle4$:

$\angle6$ lies between line $l$ and line $m$, and $\angle4$ lies between line $l$ and the transversal $t$. They are not in the correct position for same - side interior angles.

• For $\angle5$ and $\angle1$:

$\angle5$ lies between line $l$ and line $m$, and $\angle1$ lies between line $l$ and the transversal $t$. They are not in the correct position for same - side interior angles.

• For $\angle8$ and $\angle2$:

$\angle8$ lies between line $l$ and line $m$, and $\angle2$ lies between line $l$ and the transversal $t$. They are not in the correct position for same - side interior angles.

Wait, there is a mistake. Let's re - analyze:
Same - side interior angles:
If we consider lines $l$ and $m$ and transversal $t$.
Same - side interior angles are pairs of angles that are on the same side of the transversal and between the two lines.
For $\angle4$ and $\angle5$:
They are between lines $l$ and $m$ and on the same side of the transversal $t$.

Answer:

$\angle5$ and $\angle4$