Question

in the figure shown at the right, lines l and m are parallel.
what type of angles do the angle pair of ∠2 and ∠4 form?
alternate exterior
same - side interior
alternate interior
linear pair
vertical angles
corresponding angles
same - side exterior
4 multiple choice 9 points
in the figure shown at the right, lines l and m are parallel.
what type of angles do the angle pair of ∠3 and ∠6 form?
same - side interior
alternate exterior
linear pair
corresponding angles
same - side exterior
vertical angles
alternate interior

Explanation:

First Question (∠2 and ∠4)

To determine the angle pair type:

• Alternate exterior: Angles on opposite sides of transversal, outside parallel lines. ∠2 and ∠4 are not exterior.
• Same - side interior: Angles on same side of transversal, between parallel lines. ∠2 and ∠4 do not fit.
• Alternate interior: Angles on opposite sides of transversal, between parallel lines. ∠2 (between \( l, m \), left of transversal) and ∠4 (between \( l, m \), right of transversal) fit.
• Linear pair: Adjacent, supplementary. ∠2 and ∠4 are not adjacent.
• Vertical angles: Opposite, equal. ∠2 and ∠4 are not vertical.
• Corresponding angles: Same position relative to transversal/parallel lines. ∠2 and ∠4 do not match.
• Same - side exterior: Angles on same side, outside. ∠2 and ∠4 are interior.

So ∠2 and ∠4 are alternate interior angles.

To determine the angle pair type:

• Same - side interior: Angles on same side of transversal, between parallel lines. ∠3 (between \( l, m \), left of transversal) and ∠6 (between \( l, m \), right of transversal) are on opposite sides, so no.
• Alternate exterior: Angles outside parallel lines. ∠3 and ∠6 are interior.
• Linear pair: Adjacent, supplementary. ∠3 and ∠6 are not adjacent.
• Corresponding angles: Same position. ∠3 and ∠6 do not match.
• Same - side exterior: Angles outside, same side. ∠3 and ∠6 are interior.
• Vertical angles: Opposite, equal. ∠3 and ∠6 are not vertical.
• Alternate interior: Angles on opposite sides of transversal, between parallel lines. ∠3 (left of transversal, between \( l, m \)) and ∠6 (right of transversal, between \( l, m \)) fit.

Answer:

Alternate interior (the option "Alternate interior")

Second Question (∠3 and ∠6)