Explanation

This combines the exterior-angle and diagonal-count formulas for regular polygons. Each interior angle 135° means each exterior angle is 180° - 135° = 45°, so the polygon has 360/45 = 8 sides (a regular octagon). The number of diagonals is n(n-3)/2 = 8 × 5/2 = 20. Option (a) 54 would be the diagonal count of a 12-sided polygon — a trap for miscomputing n. Hence option (c).