Answer: 2 solutions
Explanation:
To find the angle of a regular polygon, use the formula 180(n-2)/n (where n is the amount of sides.)
Setting them equal, we get (180n-360)/n = 1680.
Multiplying by n on both sides, we get 180n-360 = 1680n.
Solving, we get 1500n = 360.
n = 0.24, which means it is not a shape, as you cannot have a shape with 0.24 sides.
The other way to look at it is to take full revolutions of 360 away from each angle, giving us 240 (the smallest remainder without it going negative). However, all the angles would be concave. If all the angles are concave, then it might connect backwards.
Subtracting 240 from 360 (to get the "exterior" angles, we get 120. Plugging it in to our equation 180(n-2)/n and solving, we get 180n-360 = 120n, and solving gives us 60n = 360, or n=6.
Since the amount of sides came together cleanly, we can classify this polygon as a normal hexagon, which has 6 sides.