In an article from the University of Chicago, July 17, 2020, it is stated that
"Judging cosmic distances from Earth is hard. So instead, scientists measure the angle in the sky between two distant objects, with Earth and the two objects forming a cosmic triangle. If scientists also know the physical separation between those objects, they can use high school geometry to estimate the distance of the objects from Earth."
That seems straightforward, except for the fact that high school geometry only works in flat space where the angles enclosed by a triangle add up to precisely 180 degrees. In a curved universe, a triangle can enclose either more or less than 180 degrees. Unless the curvature is known, triangulation shouldn't work reliably in a curved space.
So my question is: in measurements of the Hubble Constant by the triangulation method, what assumptions are made about curvature of the universe? And, how well-founded are those assumptions?