Since $GI \parallel JL$, and the angle $\angle LKM = 121^\circ$, we can apply some geometric principles.

Assuming that point $K$ lies on the transversal that intersects the parallel lines $GI$ and $JL$, the angle $\angle LKM = 121^\circ$ can be used to determine the measure of other angles. Typically, angles on a straight line sum to $180^\circ$. Therefore, $\angle LKH$ would be the supplementary angle to $\angle LKM$, since they form a linear pair.

Thus, we calculate: $m\angle LKH = 180^\circ - m\angle LKM = 180^\circ - 121^\circ = 59^\circ$

So, $m\angle LKH = 59^\circ$.

Would you like further explanation or have any questions about this solution?

Related Questions:

1. What is a linear pair of angles?
2. How do supplementary angles work?
3. How can parallel lines help in angle determination?
4. What are corresponding angles and how are they useful?
5. How do you find alternate interior angles?

Tip:

When working with parallel lines, always look for corresponding, alternate interior, and supplementary angles to simplify your problem.