Question

Draw a pentagon and a line n such that $R_n$ maps the pentagon to itself.

Short answer

Dotted line is the line of reflection.

Step-by-step solution

Step 1. Given Information.

After reflection the image is same as previous.

Step 2. Explanation.

Choose a pentagon with length of all side equal, now taking the mid-point of any of its side, and drawing a line from that point to a vertex opposite to it.

Now using the new line as the line of reflection, the same figure can be obtained, as the two part of the figure are isometric to each other.

Step 3. Conclusion.

Hence, the dotted line is the line of reflection.