Two angles of an isosceles triangle measure $70^\circ$ and $x^\circ$. What is the sum of the three possible values of $x$?
$\textbf{(A)}\   95    \qquad \textbf{(B)}\    125   \qquad \textbf{(C)}\    140   \qquad \textbf{(D)}\    165   \qquad \textbf{(E)}\     180$
There are 3 cases: where $x^\circ$ is a base angle with the $70^\circ$ as the other angle, where $x^\circ$ is a base angle with $70^\circ$ as the vertex angle, and where $x^\circ$ is the vertex angle with $70^\circ$ as a base angle.
Case 1: $x^\circ$ is a base angle with the $70^\circ$ as the other angle:
Here, $x=70$, since base angles are congruent.
Case 2: $x^\circ$ is a base angle with $70^\circ$ as the vertex angle:
Here, the 2 base angles are both $x^\circ$, so we can use the equation $2x+70=180$, which simplifies to $x=55$.
Case 3: $x^\circ$ is the vertex angle with $70^\circ$ as a base angle:
Here, both base angles are $70^\circ$, since base angles are congruent. Thus, we can use the equation $x+140=180$, which simplifies to $x=40$.
Adding up all the cases, we get $70+55+40=165$, so the answer is $\boxed{\textbf{(D)}\    165}$.