You cannot since there is not enough information.
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The golden ratio, phi occurs many places in the platonic solids. The dihedral angle on the dodecahedron is 2*atan(phi), and the dihedral angle on the icosahedron is 2*atan(phi2) or 2*atan(phi + 1). The mid radius of the dodecahedron is similarly phi2/2 or (phi + 1)/2, and the mid radius on the icosahedron is phi/2. There are several other measures within Platonic solids which involve phi.
An angle does not have a mid point.
Normally it's its centre which is at the mid point of its diameter.
It is the mid-point of a line segment that has end points
mid condition! Its a confusing play on words!!