Question

① and ∠6 are alternate interior angles. ② ∠2 and are alternate exterior angles. > identify the pair of congruent angles in each diagram. ⑤ ≅ ∠3 ⑥ ≅

Explanation:

Step1: Recall alternate - interior angles definition

Alternate - interior angles are formed when a transversal intersects two parallel lines and are on the inside of the two parallel lines and on opposite sides of the transversal. In the second diagram, $\angle3$ and $\angle6$ are alternate - interior angles.

Step2: Recall alternate - exterior angles definition

Alternate - exterior angles are formed when a transversal intersects two parallel lines and are on the outside of the two parallel lines and on opposite sides of the transversal. In the first diagram, $\angle2$ and $\angle7$ (not labeled in the given, but in a typical parallel - line and transversal setup) would be alternate - exterior angles. For the given diagrams, $\angle2$ and $\angle7$ (assuming a complete labeling) are alternate - exterior angles.

Step3: Recall congruent - angles properties for parallel lines

When a transversal intersects two parallel lines, alternate - interior angles are congruent and alternate - exterior angles are congruent. In the first diagram, $\angle1\cong\angle3$ (corresponding angles) and $\angle2\cong\angle4$ (corresponding angles). In the second diagram, $\angle4\cong\angle6$ (alternate - interior angles) and $\angle5\cong\angle3$ (alternate - interior angles).

Answer:

1. $\angle3$
2. (Assuming a complete labeling) $\angle7$
3. $\angle1$
4. $\angle4\cong\angle6$ (or $\angle5\cong\angle3$)