There are only a handful of stars where we can measure the angular size directly. It's far more common to measure the distance, the temperature (-> surface brightness) and apparent brightness of stars. Combined they tell us the radius of the object. That knowledge then be applied to stars too far away to measure the distance directly.

For exoplanets the brightness in images can still be useful, but the most accurate radius measurements come from transits: We measure which fraction of the starlight is blocked, so we can use the radius of the star to measure the radius of the planet.