1. **State the problem:** We have two similar quadrilaterals IJKL and MNOP. Given side lengths IJ = 13, LK = 19 in IJKL, and side NO = 59 in MNOP, we need to find the measure of side NO in MNOP. 2. **Recall the property of similar figures:** Corresponding sides of similar figures are proportional. This means the ratio of one side in IJKL to its corresponding side in MNOP is the same for all pairs of corresponding sides. 3. **Identify corresponding sides:** Since quadrilaterals are named in order, side IJ corresponds to side MN, and side LK corresponds to side OP. Given NO = 59, we want to find the length of NO, which corresponds to side JK in IJKL. 4. **Set up the proportion:** We know LK corresponds to OP, so $$\frac{LK}{OP} = \frac{IJ}{MN} = \frac{JK}{NO}$$ Given LK = 19, NO = 59, and IJ = 13, we can find the scale factor between the quadrilaterals using sides LK and OP or IJ and MN. However, since NO corresponds to JK, and NO is given as 59, we need the length of JK in IJKL to find NO. 5. **Assuming JK corresponds to NO:** Since NO = 59, and JK is unknown, we can find the scale factor using known sides IJ and MN or LK and OP if those lengths were given. But since only IJ and LK are given in IJKL and NO in MNOP, and no other side lengths in MNOP are given, we assume the scale factor is $$k = \frac{NO}{JK}$$. 6. **Since JK is not given, but the problem states to find NO, and NO is given as 59, it seems the problem wants the length of NO, which is already 59.** 7. **If the problem meant to find the length of side NO corresponding to JK, and JK is unknown, we cannot solve without JK.** **Conclusion:** Based on the information, side NO is 59 as given. **Final answer:** $$\boxed{59}$$