question_answer

In the adjoining 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) \[\therefore \]\[x+x+70=180\] (sum of the angles of a triangle is \[180{}^\circ \]) \[\Rightarrow \]   \[2x=110\]\[\Rightarrow \]\[x=55\] \[\angle CDB=55{}^\circ .\]