Hi,
So I am slightly confused by some of the lettering, but perhaps I am missing something. If you are told that [itex]\angle BON = 65[/itex], then do you understand the working to find [itex]\angle AOC = 30 degrees[/itex] (I am assuming point C is where point N is)?
If we can accept that, then I think the easiest way to get [itex]\angle BOA[/itex] is just to consider [itex]\angle BON = \angle BOA + \angle AON[/itex]. Solving this yields the same answer of 35 degrees.
I believe they have labeled the 115 degrees by using the fact that line segments BA and ON are parallel and [itex]\angle OBA[/itex] and [itex]\angle BON[/itex] are therefore supplementary ('internal' angles of parallel lines add up to 180 degrees), so they could get 115 from [itex]\angle OBA = 180 - 115[/itex]
Hope that answers your question. If not, let me know and I will respond appropriately.
Kind regards