Where would an imaginary line need to be drawn to reflect across an axis of symmetry so that a regular pentagon can carry onto itself? a) any angle to any angle b) any angle to the farthest angle c) any angle to the next closest angle d) any angle to the center of the side opposite the angle

To illustrate, I’ve printed out a paper hexagon and creased it along the axes of symmetry listed in your question. When we say a shape can “carry onto itself,” we mean that reflecting it along a specific line will keep the shape’s position and orientation completely identical to how it started. If you can imagine creasing and folding the shape along that line, the shapes on either side of the fold would be exactly the same.

As you can see from my example, a line from an angle to the midpoint of one of the pentagon’s sides I the only fold that meets this requirement.