If your pyramid parts have a base edge cut at 15º this means the sides form an angle (lean inwards from the base line) at 75º. By saying pyramid I assume you're talking of a four sided structure.
Therefore the first number you require is 93.8º for the dihedral angle which means to mitre the four meeting corners you divide the dihedral angle by 2 = 46.9º. Cut the long rising edges at this, i.e., 46.9º from the outer face of the pyramid face board to the inner face of the board.
The other angle you need is the mitre angle which is 75.5º. This is the angle required between the bottom edge of each pyramid piece and each edge rising from that bottom edge.
Note that for all of the above given angles if you can cut them to within half a degree accuracy you'll be doing pretty well, e.g., don't get too upset if your attempted 75.5º cut given just above comes out anywhere between 75º and 76º.
If your base, presumably with a cut off top to carry the cake stand, has either more or less sides than four it's not a top sawn off square pyramid type structure (frustum) but some other form of polyhedron, e.g., triangular frustum, hexagonal frustum, and so on. Slainte.
