Some rounding error, I think, maybe because the "184" in the last two lines is missing the ".5"? I got x ≈ 84.74°, but anyway, that's not the angle the problem is asking -- angle x is angle RPQ, and this is the angle that they want (the angle is marked with "**") in the diagram (click below):

This angle is easy to find.

For part (B), you drop a perpendicular from R to PQ, as in this diagram (click below):

$\displaystyle \triangle PRS$ is a right triangle, and PR, its hypotenuse, is 184.5, so you should be able to find the length RS.