Question

Two angles of an isosceles triangle measure $70^\circ$ and $x^\circ.$ What is the sum of the three possible values of $x?$

$95$

$125$

$140$

$165$

$180$

All the following possibilities are shown below.

In the first scenario, we get $x = 70$ by the properties of the isosceles triangle.

In the second scenario, we get that $70 \cdot 2 + x = 180,$ from which we get that $x = 40.$

From the third scenario, we get that $2x + 70 = 180,$ from which we get that $x = 55.$

The sum of these values yields $70 + 40 + 55 = 165.$

Thus, D is the correct answer.