1. Let's state the problem: A regular hexagon has several lines of symmetry, and we want to find how many lines of symmetry it has and the angle between any two adjacent lines of symmetry. 2. A regular hexagon has 6 equal sides and 6 equal angles. It is a highly symmetric shape. 3. The lines of symmetry of a regular hexagon include the lines through opposite vertices and the lines through the midpoints of opposite sides. 4. Since there are 6 vertices and 6 sides, a regular hexagon has exactly 6 lines of symmetry. 5. These 6 lines of symmetry are evenly spaced around the center of the hexagon. 6. The total angle around a point is $360^\circ$. 7. Therefore, the angle between any two adjacent lines of symmetry is the total angle divided by the number of lines of symmetry: $$\frac{360^\circ}{6} = 60^\circ.$$ Answer: A regular hexagon has 6 lines of symmetry, and the angle between any two adjacent lines of symmetry is $60^\circ$.