Question

describing congruent angle relationships

use the diagram to fill in the missing angle that makes the sentence true.

1      and (angle5) are corresponding angles.
2 (angle7) and      are corresponding angles.
3 (angle8) and      are corresponding angles.
4      and (angle6) are corresponding angles.
5      and (angle6) are alternate interior angles.
6 (angle3) and      are alternate interior angles.
7 (angle2) and      are alternate exterior angles.
8      and (angle7) are alternate exterior angles.

Explanation:

Step1: Recall corresponding - angles definition

Corresponding angles are in the same relative position with respect to the transversal and the parallel lines.

Step2: Find corresponding - angles

1. $\angle1$ and $\angle5$ are corresponding angles.
2. $\angle7$ and $\angle3$ are corresponding angles.
3. $\angle8$ and $\angle4$ are corresponding angles.
4. $\angle2$ and $\angle6$ are corresponding angles.

Step3: Recall alternate - interior - angles definition

Alternate interior angles are between the two parallel lines and on opposite sides of the transversal.

Step4: Find alternate - interior - angles

1. $\angle4$ and $\angle6$ are alternate interior angles.
2. $\angle3$ and $\angle5$ are alternate interior angles.

Step5: Recall alternate - exterior - angles definition

Alternate exterior angles are outside the two parallel lines and on opposite sides of the transversal.

Step6: Find alternate - exterior - angles

1. $\angle2$ and $\angle8$ are alternate exterior angles.
2. $\angle1$ and $\angle7$ are alternate exterior angles.

Answer:

1. $\angle1$
2. $\angle3$
3. $\angle4$
4. $\angle2$
5. $\angle4$
6. $\angle5$
7. $\angle8$
8. $\angle1$