Question

parallel lines m and n are intersected by parallel lines p and q.
which angles are alternate interior angles? choose the correct answer.
a) ∠1 and ∠14
b) ∠6 and ∠9
c) ∠7 and ∠11
d) ∠4 and ∠13

Explanation:

Step1: Recall alternate interior angles definition

Alternate interior angles are formed when a transversal crosses two parallel lines. They lie between the two parallel lines (interior) and on opposite sides of the transversal (alternate).

Step2: Analyze each option

• Option A: $\angle 1$ and $\angle 14$: $\angle 1$ is on line \( m \), $\angle 14$ is on line \( n \), but they are not between the two pairs of parallel lines in a way that fits alternate interior (transversal here would be \( p \) or \( q \), but their positions don't match).
• Option B: $\angle 6$ and $\angle 9$: Lines \( m \) and \( n \) are parallel, transversal is \( p \). $\angle 6$ is between \( m \) and \( n \) (interior), $\angle 9$ is also between \( m \) and \( n \), and they are on opposite sides of transversal \( p \). This fits alternate interior angles.
• Option C: $\angle 7$ and $\angle 11$: $\angle 7$ is on line \( m \), $\angle 11$ is on line \( n \), but their positions relative to transversal \( q \) don't form alternate interior (they are not between the two parallel lines in the correct way).
• Option D: $\angle 4$ and $\angle 13$: $\angle 4$ is on the upper part, $\angle 13$ is on the lower part, not between the parallel lines as alternate interior.

Answer:

B) $\angle 6$ and $\angle 9$