In a regular quadrangular pyramid, the angle between the opposite side faces is 40 (degrees)

In a regular quadrangular pyramid, the angle between the opposite side faces is 40 (degrees). Find the angle of inclination of the side faces to the base plane?

The side faces of a regular pyramid are isosceles triangles.

Let us draw apothems KH and KM of the lateral faces KСD and KAB.

Since the faces of the pyramid are equal, the lengths of the apothems are also equal. The apothems of the side faces are the heights of an isosceles triangle, then the linear angle MKH is equal to the dihedral angle between the side faces. Angle MKH = 40.

The dihedral angle between the side face and the base is equal to the linear angle KM of the isosceles triangle MKH.

Angle KHM = (180 – MKH) / 2 = (180 – 40) / 2 = 70.

Answer: The tilt angle is 70.