To determine the bond angles and molecular geometry of methane CH4 using quantum chemistry principles, we can use the Valence Shell Electron Pair Repulsion VSEPR theory. This theory states that the electron pairs around a central atom will arrange themselves to minimize repulsion, thus determining the molecular geometry.1. Determine the central atom: In methane, the central atom is carbon C .2. Count the valence electrons: Carbon has 4 valence electrons, and each hydrogen atom has 1 valence electron. Since there are 4 hydrogen atoms, there are 4 valence electrons from hydrogen. In total, there are 8 valence electrons in methane.3. Distribute the valence electrons: Carbon forms 4 single bonds with 4 hydrogen atoms, using all 8 valence electrons.4. Determine the electron pair geometry: In methane, there are 4 bonding electron pairs around the central carbon atom. According to VSEPR theory, these electron pairs will arrange themselves to minimize repulsion. The arrangement that minimizes repulsion for 4 electron pairs is a tetrahedral geometry.5. Determine the molecular geometry: Since there are no lone pairs on the central carbon atom, the molecular geometry is the same as the electron pair geometry, which is tetrahedral.6. Calculate the bond angles: In a tetrahedral geometry, the bond angles between the electron pairs are approximately 109.5 degrees.So, the molecular geometry of methane CH4 is tetrahedral, with bond angles of approximately 109.5 degrees.