Why the bond angle of methane is 109 instead of 90?

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scientist91
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I know that the sp3 hybrid orbitals form 109 angle, but why the angle is not 90. If the angle is 109 the repulsion is minimized or what? Show some comparations. Thank u.
 
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I believe your problem lies in the fact that you are only looking in two dimensions. What orbital theory are you using? Valence shell theory is useless for all practical applications anyway.
 
3 Dimensions

Indeed, in 3d space four points equally spaced around a center point form a tetrahedron, not a square, hence your bond angle of 109.5 degrees.
 
methane consists of four bonded pairs, i.e 4 C-H bonds. So as to minimize repulsion, the molecule adopts a tetrahedral shape, hence bond angle becomes 109.5. with bond angle of 90, the molecule would not be very stable.