1. **State the problem:** We have a laser beam inside an optical fibre with parallel sides. The beam bounces off the sides at the same angle it hits them. Given the angle of incidence is 46°, we need to find the size of angle $x$ at the last bounce. 2. **Key rule:** The angle of incidence equals the angle of reflection. Since the sides are parallel, the beam forms alternate interior angles with the fibre sides. 3. **Analyze the angles:** Each bounce creates an angle of 46° with the fibre side. Because the fibre sides are parallel, the angle $x$ at the last bounce is equal to the angle of incidence or reflection. 4. **Conclusion:** Therefore, angle $x = 46^\circ$. **Final answer:** $$x = 46^\circ$$