Isosceles triangles

Geometry Level 3

For some value \(d,\) an isosceles triangle has at least one angle of \((2d-40)\) degrees and at least one angle of \((d+20)\) degrees.

For each of such triangles, let \(\alpha\) denote the smallest angle in degrees. Then what is the sum of all possible \(\alpha\)'s?

Excel in math and science