In the figure, AB and CD are parallel, the measure of angle D is twice that of angle B, AD is of length *a* and CD is of length *b*. What is the length of AB in terms of *a* and *b*?

*a*/2 + 2*b*- 3
*b*/2 + 3*a*/4 - 2
*a*–*b* - 4
*b*–*a*/2 *a*+*b*

∠B + ∠C = 180°, so D2 + ∠C = 180° and ED || BC.

BCDE is a parallelogram → EB = *b*.

E1 = B (corresponding angles) → E1 = D1 = D2,

so △AED is isosceles → AE = *a*

AB = AE + EB = *a* + *b*.

The answer is (e).