To determine which angle of polygon \( P \) is congruent to a specific angle after the polygon has undergone a rotation, we would generally need to know the specific angles of polygons \( P \) and \( P' \) (the image of \( P \) after rotation), as well as the rotation angle used.
However, assuming that the rotation preserves the angles (which it does), each angle of the original polygon \( P \) will be congruent to its corresponding angle in the rotated polygon \( P' \).
Typically, if there is a specific angle in question (let's say \(\angle X\)), you would compare \(\angle X\) to the angles of polygon \( P' \) to see which one matches.
If you could provide the details of the angles or additional context, I could help identify exactly which angle is congruent. But given the choices A, B, C, and D (for angles \( \angle K, \angle L, \angle M, \angle N \)), we would need information about the angles in polygons \( P \) and \( P' \) to give a definitive answer.