1. **Problem Statement:** Given rectangle KLMN with angles \(\angle K = 47^\circ\) and \(\angle N = 57^\circ\), find the value of \(\angle KMO\) where point O lies on side KN. 2. **Understanding the Rectangle:** In rectangle KLMN, all angles are right angles (90°). Points K, L, M, N form the rectangle with KM and NM as diagonals. 3. **Key Properties:** - Opposite sides are equal and parallel. - Diagonals in a rectangle are equal in length. - Angles at K and N given are angles formed by diagonals and sides. 4. **Analyzing the Angles:** - \(\angle K = 47^\circ\) is the angle between side KL and diagonal KM. - \(\angle N = 57^\circ\) is the angle between side NM and diagonal NM. 5. **Finding \(\angle KMO\):** Since O lies on KN, and KM is a diagonal, \(\angle KMO\) is the angle between KM and MO. 6. **Using Triangle KMO:** - Since O is on KN, segment KO + ON = KN. - \(\angle KMO\) is the angle at M between points K and O. 7. **Using angle sum in triangle KMO:** - The sum of angles in triangle KMO is 180°. - Using given angles and properties, \(\angle KMO = 14^\circ\). **Final answer:** \(\boxed{14^\circ}\) which corresponds to option C.