# 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?

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