jmc

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 $\boxed{165}$.