$2$ planes and angle between them

Question

IF I have two $3d$ planes such as Oab and Oa'b'. If these two planes intersect a horizontal plane and the intersection of each plane makes AB and A'B' lines. then,

1. Does the angle between AB, A'B' i.e. APA' is equal to the angle between normal vectors (i.e. n1 and n2) of the planes?

2. Does this scenario is always true, even if we intersect these two planes with third plane which is not horizotal (i.e. instead of XY , if there is oblique plane)?

Please, answer my both questions.

Answer 1

It is not, in general, true that the angle between the normal vectors $n_1$ and $n_2$ of two planes is equal to the angle between the lines of intersection $AB$ and $A′B′$ of these two planes with a third plane.

For example, you may have two non-parallel planes which intersect the XY plane in parallel lines.

Also, there is nothing special about the XX-plane being 'horizontal'.