Question

5 multiple choice 10 points what is the relationship between ∠3 and ∠6? ¿cuál es la relación entre ∠3 y ∠6? \\(\overleftrightarrow{cf} \parallel \overleftrightarrow{jk}\\) diagram: two parallel lines cf (c left, f right) and jk (j left, k right) cut by a transversal. angles labeled 1 (top-left at cf), 2 (top-right at cf), 3 (bottom-left at cf), 4 (bottom-right at cf); 5 (top-left at jk), 6 (top-right at jk), 7 (bottom-left at jk), 8 (bottom-right at jk). options: alternate exterior angles (ángulos exteriores alternos), corresponding angles (ángulos correspondientes), alternate interior (ángulos interiores alternos), vertical angles (ángulos verticals), same side exterior (ángulos exteriores del mismo lado)

Explanation:

To determine the relationship between \( \angle 3 \) and \( \angle 6 \), we analyze their positions relative to the parallel lines \( \overleftrightarrow{CF} \) and \( \overleftrightarrow{JK} \) and the transversal. Alternate Interior Angles are non - adjacent angles that lie between the two parallel lines and on opposite sides of the transversal. \( \angle 3 \) and \( \angle 6 \) are between the parallel lines \( CF \) and \( JK \) and on opposite sides of the transversal.

• Alternate Exterior Angles lie outside the two parallel lines, so this is not the case for \( \angle 3 \) and \( \angle 6 \).
• Corresponding Angles are in the same relative position at each intersection, which is not true for \( \angle 3 \) and \( \angle 6 \).
• Vertical Angles are opposite each other when two lines intersect, and \( \angle 3 \) and \( \angle 6 \) are not formed by the same two intersecting lines in that way.
• Same - Side Exterior Angles lie outside the parallel lines and on the same side of the transversal, which is not the case here.

So, \( \angle 3 \) and \( \angle 6 \) are Alternate Interior Angles.

Answer:

Alternate Interior (ángulos interiores alternos)