question_answer

In the given figure, ABCD is a rhombus. If \[\angle A=70{}^\circ ,\]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 \[\Rightarrow \]   \[\angle CBD=\angle CDB=x{}^\circ \] \[\angle BCD=\angle BAD=70{}^\circ \] (opposite angles of a rhombus) \[\therefore \]      \[x+x+70=180{}^\circ \] (sum of the angles of a triangle is 180°) \[\Rightarrow \]   \[2x=110{}^\circ \] \[\Rightarrow \]   \[x=55.\] \[\therefore \]      \[\angle CDB=55{}^\circ \]