A regular pentagon and a regular hexagon are drawn on a flat surface so that they share one complete side and do not overlap. At one end of that shared side, an interior angle of the pentagon and an interior angle of the hexagon meet. What is the size of the gap left between the two shapes at that point?

Each interior angle of a regular pentagon is (5 − 2) × 180°/5 = 108°, and of a regular hexagon (6 − 2) × 180°/6 = 120°. The angles round a point add to 360°, so the gap = 360° − 108° − 120° = 132°. Adding the two interior angles instead of subtracting gives the trap 228°, averaging them gives 114°, and 108° is just the pentagon's own angle.