Question

1. choose the correct answer.

given \\( \angle 1, \angle 2, \angle 3 \\), and \\( \angle 6 \\), which are alternate interior angles?
\\( \angle 3 \\) and \\( \angle 1 \\)
\\( \angle 3 \\) and \\( \angle 6 \\)
\\( \angle 3 \\) and \\( \angle 2 \\)
\\( \angle 1 \\) and \\( \angle 6 \\)

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 $\angle3$ and $\angle1$: $\angle1$ and $\angle3$ are adjacent angles (they form a linear pair), not alternate interior angles.
• For $\angle3$ and $\angle6$: $\angle3$ and $\angle6$ lie between lines $l$ and $m$ and on opposite sides of transversal $t$. So they are alternate interior angles.
• For $\angle3$ and $\angle2$: $\angle3$ and $\angle2$ are adjacent angles (they form a linear pair), not alternate interior angles.
• For $\angle1$ and $\angle6$: $\angle1$ does not lie between the two lines $l$ and $m$ in the correct position for alternate interior angles with $\angle6$.

Answer:

$\angle3$ and $\angle6$