There are many occasions.
At 12:00:10.9090... the hour and minte hand will be 1 degree apart.
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Fist at arms length = ~ 10 arc degrees Thumb at arms length = ~ 2 arc degrees Little finger ~ 1 arc degree
Stars do not have arms.
A central angle has its vertex at the center of a circle, and two radii form the Arms. Central angle AOC is described as subtended by the chords AC and by the arc AC. An inscribed angle has its vertex on the circle, and two chords form the arms. Inscribed angle ABC is also described as subtended by the chord AC and by the arc AC.
When an angle is drawn a small arc is normally placed near the vertex between the arms to show the angle. A reflex angle is one greater than 180°, so draw the two arms as normal and then draw a small arc around the vertex of the angle "outside" the arms of the angle, ie around the angle which is greater than 180° If the problem is how to draw the reflex angle with a protractor that only goes up to 180°, then note that "360° - the reflex angle" gives an angle which is less than 180° and can be measure by the 180° protractor. Draw one arm of the angle, measure the calculated angle (eg if the reflex angle was 200°, 360° - 200° = 160°, so measure 160°), draw the other arm, and then draw an arc around the vertex "outside" the arms to show the reflex angle (in the example, the 200° angle).
Ignoring the reflex nature of it going lots of times round, 6910 mod 360 = 70 70° is an acute angle → the final angle between the arms of 6910° is an acute angle.