Why is the Cl-C-Cl bond angle smaller than H-C-H in dichloromethane?

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How is the bond angle for Cl-C-Cl in dichloromethane different from H-C-H bond angle of CH4? Is it smaller??
 
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Chlorine has three free electron pairs, hydrogen has none. Because of the electon pairs chlorine atoms repell from each other more strongly so the Cl-C-Cl bond angle should be bigger than H-C-H. I am not sure of this, but it seemed logical to me.