Calcute angle between two planes of a hexagonal pyramid

Are you supposed to do this analytically? If so, have you thought about setting up a convenient coordinate system?
For the first one, the dihedral angle will be the angle between the altitudes of any two connected triangle faces (the angle you showed is ~~complementary~~ supplementary), with the opposing side being an inner diagonal of the base. You can find the altitudes of the faces if you can find the length of each edge and area of each face.

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