A point P is selected at random from the interior of the pentagon with vertices A=(0,2), B=(4,0), C=(2 \pi+ 1,0), D=(2 \pi+1,4), and E=(0,4). What is the probability that \angle A P B is obtuse?

**Answer Choices**

A. \dfrac{1}{5}

B. \dfrac{1}{4}

C. \dfrac{5}{16}

D. \dfrac{3}{8}

E. \dfrac{1}{2}