Good Quadrilaterals

Case 1: Two non-adjacent sides. There are $\binom{50}{2}$ pairs of sides, of which 50 have adjacent sides. $\binom{50}{2}$ - 50 = 1175 quadrilaterals.

Case 2: Two adjacent sides. There are 50 pairs of adjacent sides. Each of these quadrilaterals has three vertices determined by the two adjacent sides. To make this case different from case 1, the final vertex can be chosen from the 45 vertices not included in or adjacent to the first three. 50*45 = 2250 quadrilaterals.

1175 + 2250 = 3425 total quadrilaterals.

There are three cases:

(1) three adjacent sides (total 50 of those)

(2) two adjacent sides, but not three (50 places the adjacent sides can be, then for each of those locations 45 places for the remaining vertex - 2250 total)

(3) two non-adjacent sides (50 places the first side can go, 45 places for each of those for the second side, but that counts each pair twice so divide by 2 - 1125 total)