question_answer

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

Correct Answer: B

Solution :

(b): The figure in question may confuse us. But actually the figure is: \[ABCE\text{ }is\text{ }a\text{ }\parallel gm\] \[~=AB=CE\] Thus in \[{{\Delta }^{1e}}CDE,\]all sides are equal \[=\angle ECD={{60}^{{}^\circ }}\] \[=\angle BCD-\angle BCE+\angle ECD\] \[={{105}^{{}^\circ }}+{{60}^{{}^\circ }}={{165}^{{}^\circ }}.\]