Question

identify all pairs of angles of the given type.

1. corresponding.
2. alternate interior.
3. alternate exterior.
4. consecutive interior.

Explanation:

Step1: Recall angle - pair definitions

Corresponding angles are in the same relative position. 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. Consecutive interior angles are between the parallel lines and on the same side of the transversal.

Step2: Identify corresponding angles

Corresponding angle pairs are $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$.

Step3: Identify alternate - interior angles

Alternate - interior angle pairs are $\angle3$ and $\angle6$, $\angle4$ and $\angle5$.

Step4: Identify alternate - exterior angles

Alternate - exterior angle pairs are $\angle1$ and $\angle8$, $\angle2$ and $\angle7$.

Step5: Identify consecutive - interior angles

Consecutive - interior angle pairs are $\angle3$ and $\angle5$, $\angle4$ and $\angle6$.

Answer:

1. Corresponding angles: $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$
2. Alternate interior angles: $\angle3$ and $\angle6$, $\angle4$ and $\angle5$
3. Alternate exterior angles: $\angle1$ and $\angle8$, $\angle2$ and $\angle7$
4. Consecutive interior angles: $\angle3$ and $\angle5$, $\angle4$ and $\angle6$