The number of diagonals in an n-sided convex polygon is given by n(n-3)/2. For n = 63, we get 63×60/2 = 1890 diagonals. Each vertex connects to n-3 other vertices via diagonals, and we divide by 2 to avoid double-counting. Option A (1953) and C (3720) are incorrect calculations; B (8906) is far too large.