In the diagram, two circles, each with center D, have radii of 1 and 2. The total area of the shaded regions is \frac{5}{12} of the area of the larger circle. What is a possible measure of \angle{ADC}?
Answer Choices
A. 108^\circ
B. 120^\circ
C. 90^\circ
D. 150^\circ
E. 135^\circ