Question

which of the following options is a pair of alternate interior angles? ∠6 and ∠3 ∠12 and ∠7 ∠6 and ∠12 ∠3 and ∠12

Explanation:

Step1: Recall alternate - interior angles definition

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

Step2: Analyze each option

• For $\angle6$ and $\angle3$: $\angle6$ and $\angle3$ are not alternate - interior angles. $\angle6$ is an exterior angle with respect to the lines intersected by the transversal and $\angle3$ is an interior angle, but they do not meet the criteria.
• For $\angle12$ and $\angle7$: $\angle12$ and $\angle7$ are not alternate - interior angles. They are not in the correct position with respect to the transversal and the two lines.
• For $\angle6$ and $\angle12$: $\angle6$ and $\angle12$ are not alternate - interior angles. They are not between the two relevant lines.
• For $\angle3$ and $\angle12$: $\angle3$ and $\angle12$ are alternate - interior angles. They are non - adjacent, lie between the two lines intersected by the transversal and are on opposite sides of the transversal.

Answer:

$\angle3$ and $\angle12$