Question

identify the following angles associated with the parallel lines cut by a transversal. ∠1 and ∠3 ∠1 and ∠4 ∠7 and ∠3 ∠6 and ∠3 ∠2 and ∠7 alternate exterior angles corresponding angles linear pair alternate interior angles vertical angles

Explanation:

Step1: Recall angle - pair definitions

When two parallel lines are cut by a transversal, different angle - pairs have specific relationships.

• Linear pairs are adjacent angles that form a straight - line, and their sum is 180°.
• Vertical angles are opposite each other when two lines intersect.
• Corresponding angles are in the same relative position with respect to the parallel lines and the transversal.
• Alternate interior angles are between the parallel lines and on opposite sides of the transversal.
• Alternate exterior angles are outside the parallel lines and on opposite sides of the transversal.

Step2: Analyze ∠1 and ∠3

∠1 and ∠3 are adjacent angles that form a straight - line at the intersection of line t and line m. So, ∠1 and ∠3 are a linear pair.

Step3: Analyze ∠1 and ∠4

∠1 and ∠4 are vertical angles since they are opposite each other at the intersection of line t and line m.

Step4: Analyze ∠7 and ∠3

∠7 and ∠3 are alternate exterior angles as they are outside the parallel lines m and n and on opposite sides of the transversal t.

Step5: Analyze ∠6 and ∠3

∠6 and ∠3 are alternate interior angles as they are between the parallel lines m and n and on opposite sides of the transversal t.

Step6: Analyze ∠2 and ∠7

∠2 and ∠7 are corresponding angles as they are in the same relative position with respect to the parallel lines m and n and the transversal t.

Answer:

∠1 and ∠3 - Linear Pair
∠1 and ∠4 - vertical angles
∠7 and ∠3 - alternate exterior angles
∠6 and ∠3 - alternate interior angles
∠2 and ∠7 - corresponding angles