question_answer

A diagonal of a rectangle is inclined to one side of the rectangle at \[{{25}^{o}}\]. What is the measure of the acute angle between the diagonals?

A)  \[{{25}^{o}}\]                   

B)                         \[{{40}^{o}}\] 

C)                         \[{{50}^{o}}\]                   

D)                         \[{{55}^{o}}\]

Correct Answer: C

Solution :

Since \[\angle CAB={{25}^{o}}\] \[\angle CAB={{65}^{o}}\] Let diagonals meet at O. \[\Delta \,\,OCB\] is an isosceles triangle. \[\therefore \] \[\angle OBC={{65}^{o}}\]   \[\Rightarrow \]  \[\angle BOC={{50}^{o}}\]