You can measure approximate angles in the sky using your hand. Make a closed fist and hold it at arm’s length. Your fist will subtend an angle of about 8° — coincidentally, that’s roughly the field of view seen through typical binoculars.
The width of a single finger held at arm’s length forms an angle of about 2°. The easiest celestial body for measuring modest angles is the Moon, which spans an apparent diameter of 0.5° (30′).
Directions on the sky are a little harder to grasp. For those of us in the Northern Hemisphere, due north marks the direction to the North Celestial Pole (conveniently marked by the 2nd-magnitude star Polaris). If an object lies due north of another, it lies in the direction of Polaris.
The clearest situation arises when the two objects lie in the southern sky. In that case, the body that lies farther north appears directly above the other. If the Moon passes 4° south of Mars, and they both lie in the south, then Mars appears 4° (8 Moon-widths) above the Moon.
Things get more complicated if the objects lie in a different direction. Imagine the Moon passing Venus when they are low in evening twilight. In this case, you have to look west to see the objects, and the North Celestial Pole lies above and to their right.
So, if the Moon passes due north of Venus, our satellite doesn’t appear directly above the planet. Instead, the Moon lies to Venus’ upper right, with the exact angle depending on your latitude. — Rich Talcott, Senior Editor