Two given lines $AB, AC$ including $\angle A= 60^{\circ}$ between them are intersected by a variable smooth continuous curve (red) so that angle sum $ \beta+\gamma = 150^{\circ} $ is always constant.
How do we find such a curve, assuming it exists?
If instead the angle sum is $ \beta+\gamma = 120^{\circ} $ then we have all moving transversal straight lines. Thanks in advance.
