I am not sure an examiner wants any more specifics than what is in the PHAN however this is how it makes sense to me. - This was a concept I struggled to grasp so I welcome any feedback on my current understanding. I am not going to explain why the aircraft enters a sideslip when banked assuming that part is understood. I want to explain how the dihedral angle basically takes advantage of sideslip to correct the bank.

When an aircraft enters a sideslip it is essentially flying slightly sideways with the low wing projecting into the flightpath. (keyword slightly). With such a small sideslip, it can be difficult to understand how dihedral corrects the bank so let's exaggarate the sideslip.

Imagine an aircraft flying almost completely sideways towards you with the low wing leading the way. (In a sideslip, the low wing projects forward) This type of flight is not reasonably possible but let's just imagine it for illustration purposes. The dihedral angle slopes upward so think of the tips of that low wing that is coming towards you now sloping upward due to the dihedral. The dihedral angle is usually very small however you can again exaggarate the dihedral to get the point. Try to think of that low wing angle sloping so much that you can begin to see the bottom of the low wing from your vantage point. This would not increase the angle of attack of the leading edge but rather increases the AOA of the side of the wing - exactly what you would expect for an airplane flying sideways. Now let's think about the high wing which is projecting away from the relative wind on our sideways flying aircraft. The high wing also has an upward angle due to dihedral however since it is on the outside of the sideslip, it doesn't increase the AOA like the other wing - rather the dihedral angle of that wing further exposes the top of the wing to the relative wing (decreasing AOA). The higher AOA on the low projecting wing increases lift and goes back to wings level.

Let me know what you all think??