Question

How is the angle used for parallax found?

Answer 1

Because of the changing position of the earth over a 6 month period, the perspective of stars etc. alters in relation to their distance.

Explanation:

An excellent explanation is given here

Answer 2

It’s measured against a “fixed” background of distant stars/galaxies that are assumed to be immobile.

Explanation:

From our perspective the position of a nearby star ‘jumps’ when viewed 6 months apart against this distant background. That jump is expressed as an angle, and then converted to a distance by trigonometry. For objects closer to us a shorter baseline than the diameter of the earth’s orbit is possible - see here:

It can also be measured due to the sun’s motion around the galaxy:

Is this a more useful answer?

Answer 3

It’s now occured to me you might have been asking ‘how physically do you measure an angle in space?’

Explanation:

Two methods: using the known gearing mechanism on the telescope or (in simpler amateur devices) you can get a graticule on the eyepiece.