$\angle 1 + \angle 2 = 180^\circ$
$\angle 3 = \angle 4$
Find $\angle 4.$

$\text{(A)}\ 20^\circ \qquad \text{(B)}\ 25^\circ \qquad \text{(C)}\ 30^\circ \qquad \text{(D)}\ 35^\circ \qquad \text{(E)}\ 40^\circ$
Using the left triangle, we have:
$\angle 1 + 70 + 40 = 180$
$\angle 1 = 180 - 110$
$\angle 1 = 70$
Using the given fact that $\angle 1 + \angle 2 = 180$, we have $\angle 2 = 180 - 70 = 110$.
Finally, using the right triangle, and the fact that $\angle 3 = \angle 4$, we have:
$\angle 2 + \angle 3 + \angle 4 = 180$
$110 + \angle 3 + \angle 4 = 180$
$110 + \angle 4+ \angle 4 = 180$
$2\angle 4 = 70$
$\angle 4 = 35$
Thus, the answer is $\boxed{D}$