Three mirror lines make a triangle.
For each corner we are free to choose the rotational symmetry:
|center  || (the corner at the left)|
|left|| (as seen from the center)|
|right|| (as seen from the center)|
sum of angles = o
If the sum of the corner angles is not 180o degrees, then one of the mirror lines has to be a circle arc!
What is the mirror image at a circle arc?