Question

the sketch shows two parallel lines cut by a transversal. which pair of angles are alternate interior angles? angle 2 and angle 6 angle 3 and angle 6 angle 4 and angle 6 angle 7 and angle 6

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are non - adjacent interior angles that lie on opposite sides of the transversal.

Step2: Analyze each option

• For "Angle 2 and angle 6": Angle 2 is an exterior angle (relative to the two parallel lines \(n\) and \(m\)), so this pair is not alternate interior angles.
• For "Angle 3 and angle 6": They are non - adjacent and lie on opposite sides of the transversal, and both are interior angles with respect to the parallel lines \(n\) and \(m\).
• For "Angle 4 and angle 6": They are same - side interior angles, not alternate interior angles.
• For "Angle 7 and angle 6": They are adjacent angles (a linear pair), not alternate interior angles.

Answer:

Angle 3 and angle 6