Technical Answer:
Nobody Knows
Probably the answer to your question:
51.43 Degrees
You see, to provide you with an accurate answer, I would need to know the side lengths, but no such information is given. That explains my technical answer. However, I think that your problem wants me to just assume that all sides are equal in length, making this a regular, 7-sided Heptagon.
A regular heptagon, which is a heptagon with all sides and angles equal, does indeed have lines of symmetry. A line of symmetry in a regular heptagon can be drawn from any vertex to the opposite side's midpoint. Since a regular heptagon has seven sides, the angle between each consecutive side is 360 degrees divided by 7, which is approximately 51.43 degrees.
Therefore, a heptagon has a line of symmetry every 51.43 degrees when it is a regular heptagon.
~~~Harsha~~~