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A given circle has a radius with the length of an integer, and the perimeter of a given sector in a circle is $15$.

Which of the following is NOT a possible value for the sector's central angle?

$ \theta = \cfrac{540}{π}$

$ \theta = \cfrac{2340}{π} $

$ \theta = \cfrac{720}{π}$

More than one of the answer choices is not a possible value.

All of the answer choices are possible.