Question

Why CH4 has bond angle109 degree and 28minutes and ammonia a bond angle of 107degrees and water a bond angle of 104.5degree

Answer 1

All three have 4 electron pairs in the outer shell of the central atom so with a roughly tetrahedral arrangement.
Methane has 4 bond pairs so the tetrahedron is symmetrical and the angle 109 degrees.
Ammonia has one lone pair that is entirely on the central atom and so exerts a greater leverage that pushes the bond pair in to 107 degrees.
The two lone pairs in water push the bonds in to 104 degrees.

Nitrogen and oxygen have high electronegativity making the Hydrogen atoms electron deficient. The positive hydrogens form "hydrogen bonds" to the lone pairs in adjacent molecules. This works as well between ammonia and water molecules as between water molecules themselves. Mixing also gives a higher entropy so there is a free energy decrease on mixing - it is a downhill process.