Question 1177180
**1. Given Information**

* NK is a median of triangle JMN. This means that NK bisects side JM, so JK = KM.
* IN > NM

**2. Triangle Inequality Theorem**

In any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

**3. Applying the Triangle Inequality Theorem to Triangle INK**

* IN + NK > IK 

**4. Applying the Triangle Inequality Theorem to Triangle NMK**

* NM + NK > MK

**5. Using the Given Information and Steps 3 and 4**

* Since IN > NM (given), and NK is common to both triangles INK and NMK, we can conclude that:
   IN + NK > NM + NK
* This further implies that IK > MK

**6. Relating IK and MK to JK and KM**

* We know that JK = KM (because NK is a median).
* Therefore, IK > JK

**7. Hinge Theorem**

The Hinge Theorem states that if two triangles have two congruent sides, then the triangle with the larger included angle has the longer third side.

**8. Applying the Hinge Theorem**

* In triangles JNK and KNM:
    * JN = NM (given)
    * NK = NK (common side)
    * IK > JK (from step 6)
* Therefore, by the Hinge Theorem, m∠1 > m∠2.

**Conclusion**

We have successfully proven that m∠1 > m∠2 using the given information, the Triangle Inequality Theorem, and the Hinge Theorem.