In the provided diagram, we are given:

• $m \angle LMN = 116^\circ$
• $m \angle JNM = 103^\circ$

We are asked to find $m \angle JKN$.

To solve this, we need to apply the properties of the figure, particularly considering the triangles and any supplementary or corresponding angles that help find the unknown angle.

Here’s a step-by-step breakdown:

1. Triangle $JNM$: The sum of interior angles in a triangle is always $180^\circ$. In triangle $JNM$, we already know two angles:

   • $m \angle LMN = 116^\circ$ (given)
   • $m \angle JNM = 103^\circ$ (given)

   We can find $m \angle NJM$ using the angle sum property: $m \angle NJM = 180^\circ - (116^\circ + 103^\circ) = 180^\circ - 219^\circ = 61^\circ$

2. Triangle $JKN$: Now, using the property that angles on a straight line sum to $180^\circ$, $m \angle JKN$ will be supplementary to $m \angle NJM$.

   Hence, we calculate: $m \angle JKN = 180^\circ - 61^\circ = 119^\circ$

Thus, $m \angle JKN = 119^\circ$.

Would you like any further clarification on this problem or the concepts used?

Here are 5 questions for further practice:

1. What is the sum of interior angles in any quadrilateral?
2. How do you identify supplementary angles in complex diagrams?
3. Can exterior angles help determine missing interior angles?
4. What are alternate interior angles, and how are they useful in geometric proofs?
5. How do you apply the angle sum property to polygons with more than three sides?

Tip: When dealing with polygons or figures formed by triangles, always remember that the sum of angles in a triangle is 180°, which can help find unknown angles in the overall figure.