Question

If a diagonal of a rectangle is inclined to one side of the rectangle at ${40}^{\circ }$, then the acute angle between the diagonals is _____.

• A. $80°$
• B. $70°$
• C. $75°$
• D. $60°$

Answer 1

The correct option is A $80°$



Given: In rectangle ABCD,
$\angle BAO=40°$

To find: Angle between the diagonals $\angle AODor\angle BOC$

In $\Delta$AOB
OA = OB
$\because$ Diagonals of a rectangle bisect each other
$\Rightarrow \angle OBA=\angle OAB={40}^{\circ }$(As the angles opposite to equal sides are equal)

Applying exterior angle property in $\Delta$AOB
$\angle AOD=\angle OBA+\angle OAB$
$\angle AOD=40°+40°$
$\angle AOD=80°$