If the problem is simply one of trying to understand the fact that dihedral causes the angle of attack of a dropped wing to become greater than that of the raised wing, a demonstration may be sufficient.
Take an A4 sheet of paper and fold it down the centre so that the two short edges come together. Now unfold it so that it looks like a pair of wings with dihedral. We will use this to represent our aircraft. It works best if you use a large dihedral angle (about 30 degrees).
Grasping the sheet at the tail end of the centre crease, hold it up about a foot in front of your face so that the crease is pointing directly at your right eye. Hold the paper so that it is in a non-banked attitude, and raise the front end of the crease to represent a nose up pitch attitude.
Close your left eye and look at the paper with your right eye. The view that you see is what the approaching air would see (assuming of course that air could see at all). You should be able to see the underside of both wings and the view of the left wing should be a mirror image of that of the right wing. This indicates that both wings are set at the same angle of attack.
Now rotate the front end of the crease so that it points at your (still closed) left eye and slightly drop the wing that is closest to your right eye. The view from your right eye now represents an aircraft that has dropped its left wing and is side slipping towards you. Once again the view that you have of each wing represents the view that the approaching air would have. You should be able to see more of the underside of the dropped wing and less of the underside of the raised wing. This means that the angle of attack of the dropped wing is greater than that of the raised wing.
If this difference is not obvious gradually increase the bank angle. You will eventually get a situation in which you can see the bottom of the dropped wing and the top of the raised wing.
The above process will not explain why the angles of attack change, but it should at least convince you that it is true.
To understand why the difference in angle of attack occurs we need to consider the relative airflow as being made up of two components. The first component is that due to forward motion of the aircraft. This component approaches the aircraft from directly ahead. The angle of attack between this component and each of the wings is identical.
The second component is the lateral airflow caused by the aircraft side slipping towards the dropped wing. As illustrated in Lightning Mate’s diagram, the dihedral angle causes the wingtip of the dropped wing to be higher than the root. The lateral airflow on this wing is from tip to root, so this means that the lateral airflow meets this dropped wing at a positive angle of attack. But for the raised wing the dihedral angle causes the wing root to be lower than the wingtip. The lateral airflow on this wing is from root to tip, so this causes the lateral airflow to meet the raised wing a lesser angle of attack.
The total angle of attack of each wing is the vector sum of the angles of attack of the two airflow components. The contribution made by the forward motion of the aircraft is the same for both wings. But the contribution made by the lateral (side slip) airflow is greater for the dropped wing that for the raised wing. The overall effect is that the dropped wing experiences a greater angle of attack than the raised wing.