Question

10)which pair of angles are alternate interior angles?\\( \angle 7 \\) and \\( \angle 2 \\)\\( \angle 8 \\) and \\( \angle 2 \\)\\( \angle 5 \\) and \\( \angle 4 \\)\\( \angle 6 \\) and \\( \angle 4 \\)

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are non - adjacent angles that lie between two lines and on opposite sides of a transversal.

Step2: Analyze each option

• For $\angle7$ and $\angle2$: $\angle7$ and $\angle2$ do not lie between the two relevant lines (lines $l$ and $m$) in the correct way for alternate interior angles.
• For $\angle8$ and $\angle2$: $\angle8$ and $\angle2$ do not lie between the two relevant lines (lines $l$ and $m$) in the correct way for alternate interior angles.
• For $\angle5$ and $\angle4$: $\angle5$ and $\angle4$ do not lie on opposite sides of the transversal $t$.
• For $\angle6$ and $\angle4$: $\angle6$ and $\angle4$ are non - adjacent, lie between lines $l$ and $m$, and on opposite sides of transversal $t$.

Answer:

$\angle6$ and $\angle4$