An element ' M ' reacts with chlorine to form the compound ${\mathrm{MCl}}_4$. In this compound no lone pairs are present and the bond angle is ${109}^0{28}^1$. The element M is

$$\begin{gathered} \mathrm{Cl}-\mathrm{Be}\Rightarrow {\mathrm{BeCl}}_2-{180}^0 \\ \mathrm{Si}+\mathrm{Cl}\Rightarrow {\mathrm{SiCl}}_4 \end{gathered}$$

According to VESPER theory in ${\mathrm{SiCl}}_4$ the central atom has no  lone pair nd there are four bond pairs. Hence, the shape is tetrahedral, a regular tetrahedral molecule holds that bond angle of $109°{28}^1$. 

So, here the element M is Silicon.  

Hence, the correct option is option (B) Si..