Mirror rorriM

A left-right reversed image will happen any time the light is reflected an even number of times from the object to its reflection.

So, for a flat mirror, the light is only reflected once (off of that surface). However at $90^\circ$ as in the picture above, the reflected candles (left and right) are again reflected (middle). So the middle mirror doesn't have the left-right reversal.

For $60^\circ$ the image is again reversed as the light has undergone three reflections.

Here is a picture clarifying how the image is "real" for $90^\circ$ but "reversed" for $60^\circ$ :

From the above image, the image is real for $90^\circ$ , since $90 = \frac{180}{2}$ . And, it is reversed for $60^\circ$ , since $60 = \frac{180}{3}$ . And, we can generalize that if $180^\circ$ is divided by an odd number, then the image will undergo an odd number of reflections, so it will be reversed, and if it is divided by an even number, it will undergo and even number of reflections and the image will be real.

So, the image will be "real" for any angle that satisfies, $(\frac{180}{n})^\circ$ for even $n$ .

The only answer for which this holds is $\boxed{45^\circ}$