Final answer:
A regular polygon with x sides has x lines of symmetry, as each side corresponds to a line that equally divides the shape into two mirror images.
Step-by-step explanation:
A regular polygon with x sides will have x lines of symmetry. This is because a regular polygon is defined as a polygon that is both equiangular and equilateral, meaning all its angles and sides are of equal measure. As a result, each side of the polygon can reflect over a line that bisects the angle at which two sides meet, creating a line of symmetry.
For example, a regular triangle (or equilateral triangle) has 3 lines of symmetry, one for each side. Similarly, a regular square has 4 lines of symmetry. This pattern continues such that a regular pentagon has 5, and so on. So, no matter what the value of x is (as long as it's a positive integer representing the number of sides in the regular polygon), the polygon will have exactly x lines of symmetry.