Final answer:
The question lacks clarity regarding the shape 'nrwdx' and the mathematical conditions provided. Typically, the sum of angles in a polygon is (n-2)*180°, but there is not enough information to solve for k.
Step-by-step explanation:
The student's question appears to be related to finding the value of k given an angle sum in a shape (nrwdx, which is likely a typo) and various mathematical expressions and conditions involving k. There is insufficient context to provide a direct answer because the shape of nrwdx is undefined in conventional geometry and the provided expressions need further clarity to connect them with the angle sum. Typically, determining the sum of the angles in a geometric shape is based on (n-2)*180° for an n-sided polygon. The sum mentioned is 540°, which suggests a polygon with four sides, since (4-2)*180° = 360°, but this conflicts with the given sum. It makes more sense for a five-sided polygon (pentagon), where (5-2)*180° = 540°. Without additional information or correct context, I cannot accurately solve for k or validate the expressions provided.