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 + 2b
- 3b/2 + 3a/4
- 2a – b
- 4b – a/2
- a + b
Draw DE to bisect ∠D. Then D1 = D2 = ∠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).