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  • A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between the diagonals is (A) 55º (B) 50º (C) 40º (D) 25º

A diagonal of a rectangle is inclined to one side of the rectangle at 25 ^{\circ}. The acute angle between the diagonals is
(A) 55 ^{\circ}           (B) 50 ^{\circ}           (C) 40 ^{\circ}            (D)25 ^{\circ}

Answers (1)

Answer:       [B]  50^{\circ}

Solution.
As we know that, diagonals of a rectangle are equal in length.

\therefore AC=BD                             {  \because  diagonals are equal}
\frac{1}{2}AC=\frac{1}{2}BD                        {dividing both sides by 2}
AO=BO                             { \because O is midpoint of diagonal}
\therefore \angle OBA=\angle OAB  
\angle OAB=25^{\circ}                      {Given}
\Rightarrow \angle OBA=25^{\circ} 
\angle BOC=\angle OBA+\angle OAB     {exterior angle is equal to the sum of two opposite interior angles}
=25^{\circ}+25^{\circ}=50^{\circ}
Hence the actual angle between the diagonals is 50^{\circ}.
Hence option B is correct

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