In the figure above, a shaded regular polygon is partially covered with a sheet of blank paper. If x+y=24°, how many sides does the covered polygon have? Show work that supports your answer.

The length of a rectangular board is 3 feet less than twice its width. a second rectangular board is such that each of its dimensions is the reciprocal of the corresponding dimensions of the first rectangular board. if the perimeter of the second board is one-fifth the perimeter of the first, what is the perimeter of the first rectangular board?