Question

1. ∠3 and ∠ are a linear pair.
2. ∠3 and ∠ are a linear pair.
3. ∠3 and ∠ are vertical angles.
4. ∠3 and ∠ are corresponding angles.
5. ∠3 and ∠ are alternative interior angles.
6. ∠3 and ∠ are consecutive interior angles.
7. ∠3 and ∠ have no relationship.

Explanation:

Step1: Recall linear - pair definition

A linear pair of angles are adjacent and supplementary. $\angle3$ and $\angle1$ are adjacent and form a straight - line, so they are a linear pair. Also, $\angle3$ and $\angle4$ are adjacent and form a straight - line, so they are a linear pair.

Step2: Recall vertical - angles definition

Vertical angles are opposite angles formed by the intersection of two lines. $\angle3$ and $\angle2$ are vertical angles.

Step3: Recall corresponding - angles definition

Corresponding angles are in the same relative position with respect to the transversal and the parallel lines. $\angle3$ and $\angle7$ are corresponding angles.

Step4: Recall alternate - interior - angles definition

Alternate interior angles are between the two parallel lines and on opposite sides of the transversal. $\angle3$ and $\angle6$ are alternate interior angles.

Step5: Recall consecutive - interior - angles definition

Consecutive interior angles are between the two parallel lines and on the same side of the transversal. $\angle3$ and $\angle5$ are consecutive interior angles.

Step6: Find non - related angle

$\angle3$ and $\angle8$ have no special angle relationship among the above - mentioned ones.

Answer:

1. $\angle1$
2. $\angle4$
3. $\angle2$
4. $\angle7$
5. $\angle6$
6. $\angle5$
7. $\angle8$