question_answer

In the adjoining figure, ABCD is a rhombus. If Z \[A=70{}^\circ ,\]then\[\angle CDB\]  is equal to

A)  \[65{}^\circ \]             

B)  \[55{}^\circ \]

C)  \[35{}^\circ \]             

D)  \[45{}^\circ \]

Correct Answer: B

Solution :

Let \[\angle CDB=x{}^\circ \] Then, CD=CB \[\Rightarrow \]\[\angle CBD=\angle CDB=x{}^\circ \] \[\angle BCD=\angle BAD=70{}^\circ \] (opp. angles of a rhombus) \[\therefore \]      \[x+x+70=180{}^\circ \] (sum of the angles a triangle is 18°) \[\Rightarrow \]   \[2x=110{}^\circ \] \[\Rightarrow \]   \[x=55\] \[\therefore \]\[\angle CDB=55{}^\circ \]