It seems at first as though there's not enough information to fix the angle whose size we are asked to establish - parts of the construction seem to have a lot of freedom to wander.
But as this situation is explored more it becomes apparent that the angle of interest maintains its size wherever the unconstrained parts of the diagram happen to rest.
This freedom to wander may be clear to the group almost immediately but if it is not, ask the students to reproduce the figure using the given values. This should help them appreciate what hasn't been specified, and lead them to question whether it is necessary for these to be specified.
Now they have something to explore.
Dynamic Geometry may help with enquiry, but isn't essential. Two drawings of the figure with measurements of the angle should be enough to suggest a possible general result which can then be reasoned over.
In conjunction with the problem presented the following connected result can be included : allow one fixed length chord to move around a given circle, relative to a second chord of some other fixed length. Joining the end of each chord to the opposite end of the other will produce two diagonal lines which, it turns out, intersect at the same angle regardless of the relative position of the chords.