jmc

In the accompanying figure, segments $AB$ and $CD$ are parallel, the measure of angle $D$ is twice that of angle $B$, and the measures of segments $AD$ and $CD$ are $a$ and $b$ respectively. Then the measure of $AB$ is equal to $\text{(A) }\frac{1}{2}a+2b\text{(B) }\frac{3}{2}b+\frac{3}{4}a\text{(C) }2a-b\text{(D) }4b-\frac{1}{2}a\text{(E) }a+b$