In the given figure \[\mathbf{AE}=\mathbf{BC}\] and \[\mathbf{AE}\parallel \mathbf{BC}\] and the three sides AB, CD and ED are equal in length. If \[\angle \mathbf{A}=\mathbf{10}{{\mathbf{5}}^{{}^\circ }}\], find measures of \[\angle \mathbf{BCD}:\]

• A.  \[{{138}^{{}^\circ }}\]                                  
• B.  \[{{165}^{{}^\circ }}\]
• C.  \[{{88}^{{}^\circ }}\]                       
• D.  None of these