, 2020

Isosceles triangles have two equal angles, and so the possibilities for these two triangles are:

1) The two equal angles are each equal to $70\degree$, or

2) The two equal angles are each not equal to $70\degree$.

(We note that a triangle can not have three angles measuring $70\degree$ since the sum of the three angles would be $3\times70\degree=210\degree$, which is greater than $180\degree$.)

If the two equal angles are each equal to $70\degree$, then the measure of the third angle is $180\degree-2\times70\degree=180\degree-140\degree=40\degree$.

If the two equal angles are each not equal to $70\degree$, then the sum of the measures of the two equal angles is $180\degree-70\degree=110\degree$, and so the measure of each of the equal angles is half of $110\degree$ or $55\degree$.

We note that in the first triangle, the measure of each of the two remaining angles ($70\degree$ and $40\degree$) is even, and in the second triangle, the measure of each of the two remaining angles ($55\degree$ and $55\degree$) is odd.

In the first triangle, the sum of the two equal angles is $S=70\degree+70\degree=140\degree$.

In the second triangle, the sum of the two equal angles is $T=55\degree+55\degree=110\degree$.
The value of $S+T$ is $140\degree+110\degree=250\degree$.