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        

B)  35

C)  40

D)  45

Correct Answer: A

Solution :

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