Question

which of the following angle pairs best describes angles 6 and 4 in the graphic below?
image of two parallel lines (a and b) cut by a transversal (t) with angles labeled 1,2,3,4,5,6,7,8
options:

• they are corresponding angles.
• they are same - side interior angles.
• they are vertical angles.
• they are alternate interior angles.
• they are alternate exterior angles.

Explanation:

Step1: Recall angle pair definitions

• Corresponding angles: Same position relative to transversal and parallel lines.
• Same - side interior angles: Between parallel lines, same side of transversal.
• Vertical angles: Opposite each other when two lines intersect.
• Alternate interior angles: Between parallel lines, opposite sides of transversal.
• Alternate exterior angles: Outside parallel lines, opposite sides of transversal.

Step2: Analyze angles 6 and 4

Lines \(a\) and \(b\) are parallel, transversal \(t\). Angle 4 is between \(a\) and \(b\) (interior), angle 6 is between \(a\) and \(b\) (interior). They are on opposite sides of transversal \(t\). So they fit alternate interior angles definition.

Answer:

They are alternate interior angles.