Question

A diagonal of a rectangle is inclined to one side of the rectangle at ${25}^o$. The acute angle between the diagonals is:

• A. ${40}^o$
• B. ${25}^o$
• C. ${55}^o$
• D. ${50}^o$

Answer 1

Answer: (D)

In $△BOC$,

$\angle OBC=\angle OCB$ ----- (Opposite angle of isosceles triangle)

$\angle OBC+\angle OCB+\angle BOC={180}^{\circ }$

${25}^{\circ }+{25}^{\circ }+\angle BOC={180}^{\circ }$

Therefore, $\angle BOC={130}^{\circ }$

So, $\angle AOB+\angle BOC={180}^{\circ }$--------(Linear pair)

$\angle AOB={180}^{\circ }-{130}^{\circ }$

$\angle AOB={50}^{\circ }$

So, the acute angle between the diagonal is ${50}^{\circ }$.