 
 
          Caption: How to measure angles approximately using your hand---in the form of spread hand, fist, and finger.
Now everyone's combination of hand and arm is a bit different---we are all unique---but just approximately at arm's length:
1 finger ≅ 1° 1 fist ≅ 7--10° (depends on whether you count the protruding thumb or not) 1 spread hand ≅ 18--20° (all from yours truly's own measurements).The above results are convenient for judging angles on the sky.
You CANNOT expect high accuracy/precision.
Examples of astronomical angles are:
Note: An angular diameter is the angle subtended by the diameter of a spherical astro-body (or any spherical body) as measured from some observation point which is usually the Earth for astronomy.
          Credit/Permission:  ©
          David Jeffery,
          2003 / Own work.
          Image link: Itself.
          Local file:  local link:  alien_angular.html.
          File:  Alien images file:
          alien_angular.html.