Question

1. in the diagram, lines f and g are parallel and cut by transversal h. which pair of angles are alternate interior angles? options: ∠1 and ∠5; ∠3 and ∠6; ∠2 and ∠7; ∠4 and ∠5

Explanation:

To determine alternate interior angles, we use the definition: alternate interior angles are formed when a transversal crosses two parallel lines, lying between the two lines (interior) and on opposite sides of the transversal (alternate).

• For $\angle1$ and $\angle5$: $\angle1$ is on line \( f \), $\angle5$ is on line \( g \), but $\angle1$ is not between the two lines (it's above $\angle3$), so not interior.
• For $\angle3$ and $\angle6$: $\angle3$ is on line \( f \) (above $\angle4$), $\angle6$ is on line \( g \) (below $\angle5$). $\angle3$ is not between the two lines (it's above the transversal's intersection with \( f \)), so not interior.
• For $\angle2$ and $\angle7$: $\angle2$ is on line \( f \) (below $\angle1$), $\angle7$ is on line \( g \) (above $\angle8$). $\angle2$ is not between the two lines, and $\angle7$ is not in a position to be alternate interior.
• For $\angle4$ and $\angle5$: $\angle4$ is on line \( f \) (between lines \( f \) and \( g \)), $\angle5$ is on line \( g \) (between lines \( f \) and \( g \)). They are on opposite sides of the transversal ( $\angle4$ is below the transversal on \( f \), $\angle5$ is above the transversal on \( g \)) and lie between the two parallel lines, so they are alternate interior angles.

Answer:

D. $\angle4$ and $\angle5$ (assuming the last option is D; if options are labeled as given, the correct pair is $\angle4$ and $\angle5$ from the provided choices, corresponding to the last option with that pair)