[yrznyyze] Octahedron and tetrahedron

The dihedral angle of the regular octahedron and the bond angle of the central carbon atom in sp3 hybridization (e.g. methane, with its hydrogens arranged at the vertices of a regular tetrahedron) are both 109.5 degrees.

Assuming they are the same value, create a geometric demonstration of this, maybe a visual proof.