question_answer

In the adjoining figure, ABCD is a rhombus whose diagonals intersect at O. If\[\angle OAB\,\,40{}^\circ \] and \[\angle ABO\,\,x{}^\circ ,\]then x is equal to

A)  \[50{}^\circ \]             

B)  \[35{}^\circ \]

C)  \[40{}^\circ \] 

D)  \[45{}^\circ \]

Correct Answer: A

Solution :

We know that, the diagonals of a rhombus bisect each other at right angles. So, \[\angle AOB=90{}^\circ \] Now, \[\angle OAB+\angle ABO+\angle AOB=180{}^\circ \] \[\Rightarrow \]\[40{}^\circ +x+90{}^\circ =180{}^\circ \Rightarrow x=50{}^\circ \]