A pentagon does have reflective symmetry.
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It is a regular pentagon!
If you're talking about convex polygons with equal sides (eg. equilateral triangles, squares, pentagons, hexagons, etc.), then the relationship is a very direct one. In those cases, there are as many lines of symmetry as there are points in the polygons. A triangle has three lines of symmetry, a square has four, a pentagon five, etc.
The letters S and N have point symmetry but not line symmetry.
There are 540 degrees in a regular pentagon. A pentagon consists of 5 angles and in a regular pentagon, each of the angles is 108 degrees.
A Regular Pentagon