There are a few ways you can go about it:

If you have a scrap piece of wood, you can cut it at an angle that you know is too wide and make small adjustments until it fits well in that lower corner.

You can make a few measurements to find the sides of the triangle that would form from conecting the top stair corner to the pillar and use that to calculate the lower corner angle.

You can use a speed square to get a fairly good approximation.

You can hold the handrail next to the gap at the appropriate heights and mark it with a pencil against the walls and like up the blade with the pencil marks.

However you approach it, don't worry too much about getting it perfectly flush with the walls. It is very likely that they are not flat (highly improbable that they are flat), and even a millimeter difference in position will visible change how it sits.