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We are given the following information from the diagram:

- \( m \angle LMN = 116^\circ \)
- \( m \angle JKM = 122^\circ \)
- \( m \angle JNM = 103^\circ \)

We are asked to find \( m \angle NKM \).

To solve this, we can use the fact that the sum of the interior angles of a quadrilateral is \(360^\circ\). The quadrilateral in the diagram is \( JKNM \), and we know three of the angles inside this quadrilateral: \( \angle LMN \), \( \angle JKM \), and \( \angle JNM \).

### Steps:
1. The interior angles of a quadrilateral add up to \( 360^\circ \), so:
   \[
   m \angle LMN + m \angle JKM + m \angle JNM + m \angle NKM = 360^\circ
   \]
2. Substituting the known angles:
   \[
   116^\circ + 122^\circ + 103^\circ + m \angle NKM = 360^\circ
   \]
3. Simplifying the sum of the known angles:
   \[
   341^\circ + m \angle NKM = 360^\circ
   \]
4. Solving for \( m \angle NKM \):
   \[
   m \angle NKM = 360^\circ - 341^\circ = 19^\circ
   \]

Thus, \( m \angle NKM = 19^\circ \).

If you have any questions or want further details, feel free to ask!

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### Related Questions:
1. How can you verify the interior angle sum for different polygons?
2. What is the sum of the interior angles for a pentagon, and how is it calculated?
3. What is the relationship between exterior and interior angles in polygons?
4. How do you calculate the interior angles of a regular polygon?
5. How does the sum of angles in a quadrilateral differ in non-Euclidean geometries?

### Tip:
Always ensure that the sum of angles in a polygon is consistent with the formula \( (n-2) \times 180^\circ \), where \( n \) is the number of sides.

In the diagram, m∠LMN = 116, m∠JKM = 122, and m∠JNM = 103. What is m∠NKM?

Learn how to solve a geometry problem involving the sum of interior angles in a quadrilateral. Given m∠LMN = 116°, m∠JKM = 122°, and m∠JNM = 103°, calculate the missing angle m∠NKM using the interior angle sum theorem. Suitable for students in Grades 8-10.

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