The problem involves parallel lines $KM$ and $NP$, with a transversal crossing through both, forming several angles. We are given that $m \angle NOQ = 115^\circ$ and are asked to find $m \angle KLO$.

Step-by-step solution:

1. Identify angle relationships:

   • $\angle NOQ$ is an exterior angle, and its corresponding angle on the other parallel line, $\angle KLO$, is an alternate interior angle. Alternate interior angles are equal when the lines are parallel.

2. Conclusion:

   • Since $\angle NOQ$ is $115^\circ$, by the alternate interior angle theorem, $\angle KLO$ must also be $115^\circ$.

Thus, the measure of $\angle KLO = 115^\circ$.

Would you like further explanation on any part of this solution? Here are some related questions that may deepen your understanding:

1. What are alternate interior angles and how are they identified?
2. How do transversal lines relate to parallel lines in terms of angle measures?
3. What other angle pairs (corresponding, vertical) could be identified in this diagram?
4. Can you explain the difference between supplementary and complementary angles?
5. How can you determine unknown angle measures if only one angle is provided in a parallel line system?

Tip: Always look for angle pairs formed by transversals and parallel lines, such as alternate interior, corresponding, or vertical angles. These relationships are key to solving angle problems quickly!