In this question, we need to find the measure of $\angle AJL$ given that $AB \parallel CD \parallel EF \parallel GH$ and that $\angle IKD = 119^\circ$.

Since all these lines are parallel, and we have the measure of $\angle IKD$, we can use the properties of parallel lines and transversal angles to determine the measure of other angles in the diagram.

Here’s a step-by-step solution:

1. Identify the relationship of $\angle IKD$ and $\angle AJL$: Since $AB$, $CD$, $EF$, and $GH$ are all parallel, $\angle IKD$ and $\angle AJL$ are corresponding angles with respect to a transversal. Corresponding angles between parallel lines are always congruent.

2. Apply the congruency of corresponding angles: Since $\angle IKD = 119^\circ$, it follows that $\angle AJL$ must also be $119^\circ$ because corresponding angles are equal.

3. Conclusion: Therefore, $\angle AJL = 119^\circ$.

So, the correct answer for $\angle AJL$ is 119°, with the reason being congruent angles due to corresponding angles formed by the parallel lines and the transversal.

Would you like more details, or do you have any additional questions?

Here are five related questions to deepen understanding:

1. What are the other types of angle relationships that occur with parallel lines and transversals?
2. How would the angle measures change if $\angle IKD$ were different?
3. Can alternate interior angles also be used to solve this problem? Why or why not?
4. How does the concept of supplementary angles relate to parallel lines and transversals?
5. What are some real-world applications of parallel line properties?

Tip: When working with parallel lines and transversals, always look for corresponding, alternate interior, or alternate exterior angles to identify congruent angles quickly.