Angle between slanting edges of pyramid P and its base confusion.. !enter image description here What we normally do when we find the angle between a slanting edge and a pyramid is find angle PQE, or PAE. But why is angle BAE $\neq$ PQE or PAE? Line AB is also a side of a square base ABCD and AE is part of a slanting edge. It seems odd to me. The angle must be the same? Many thanks in advance

Imagine that the height of the pyramid is very small. Then $\angle PQE$ and $\angle PAE$ each go toward 0 (though not at the same rate), whereas $\angle BAE$ goes towards $45^\circ$.