Why does Methane lack 90 degree angles?

[Physt]

With the Methane structure of CH₄ and an electron structure of Carbon as 1s²2s²2p_x¹2p_y¹ and the electron structure of Hydrogen as 1s¹ with P-orbitals separated by 90 degrees from each other and S-orbitals uniform spheres why aren't two of the Hydrogen atoms in a Methane molecule at 90 degree angles (or at some balance between there and the homogenous 109.5 degree angles shown between all Hydrogen atoms)?

 

[Khashishi]

Methane has a tetrahedral structure due to its symmetry. The carbon hydrogen bonds are SP3 hybrid bonds. http://en.wikipedia.org/wiki/Orbital_hybridisation#sp3_hybrids
There are no unbonded electron pairs on the carbon, so the bonds should distribute themselves more or less equally spaced, which gives a tetrahedron.

 

[Physt]

Methane has a tetrahedral structure due to its symmetry. The carbon hydrogen bonds are SP3 hybrid bonds. http://en.wikipedia.org/wiki/Orbital_hybridisation#sp3_hybrids
There are no unbonded electron pairs on the carbon, so the bonds should distribute themselves more or less equally spaced, which gives a tetrahedron.

Right, but if three of the bonds are hybrid bonds why are they not spaced 90 degrees from each other (or more towards 90 degrees than the even 109.5 degrees all around) with the remaining 2s bond spaced evenly away from each of them? Are the 2p shells just a rough "the bond must be within this region" and if so are the Hydrogen atoms spaced at different distances away from the Carbon atom? What I'm trying to understand is why there appears to be no relation between the orbital theory (beyond the total number of possible bonds irrespective of the angles of the bonds) and the location of atoms with regard to each other.

 

[Borek]

Right, but if three of the bonds are hybrid bonds

All four are. sp³ means mixing four bonds (one s and three p) into another four.

 

[Physt]

All four are. sp³ means mixing four bonds (one s and three p) into another four.

Thanks. Likewise for your post in the other thread.