A transversal intersects two parallel lines and forms eight angles. Which of the following statements is false?

a)alternative interior angles are always congruent.
b)corresponding angles are always congruent.
c)adjacent interior angles are always supplementary
d)exterior angles are always congruent

I need help with this question.

To determine which statement is false, we need to understand the properties of angles formed by a transversal intersecting two parallel lines.

When a transversal intersects two parallel lines, it forms eight angles as shown below:

```
1 2
--------------
3 4
--------------
5 6
--------------
7 8
```

Statement a) says that alternative interior angles are always congruent. In the diagram above, alternate interior angles are angles 3 and 6, and angles 4 and 5. If the lines are parallel, then angles 3 and 6 will be congruent, and angles 4 and 5 will also be congruent. This statement is true.

Statement b) says that corresponding angles are always congruent. Corresponding angles are angles that are in the same position relative to the transversal and the parallel lines. In the diagram above, corresponding angles are angles 1 and 5, angles 2 and 6, angles 3 and 7, and angles 4 and 8. If the lines are parallel, then corresponding angles will be congruent. This statement is true.

Statement c) says that adjacent interior angles are always supplementary. Adjacent interior angles are angles that are on the same side of the transversal and inside the two parallel lines. In the diagram above, adjacent interior angles are angles 3 and 5, angles 4 and 6, angles 5 and 7, and angles 6 and 8. If the lines are parallel, then adjacent interior angles will be supplementary, meaning their measures will add up to 180 degrees. This statement is true.

Statement d) says that exterior angles are always congruent. Exterior angles are angles that are on the outside of the two parallel lines and next to the transversal. In the diagram above, exterior angles are angles 1, 2, 7, and 8. If the lines are parallel, then the exterior angles will be congruent. However, in this case, it is false because angle 1 and angle 8 are not congruent. Therefore, statement d) is the false statement.

In conclusion, statement d) is the false statement.