Question

If a diagonal of a rectangle is inclined to one side of the rectangle at ${35}^{\circ }$, then the acute angle between the diagonals is _____.

• A. ${35}^{\circ }$
• B. ${60}^{\circ }$
• C. ${70}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is C ${70}^{\circ }$

Given: In rectangle ABCD,
$\angle BAO=35°$

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

In $\Delta$AOB
OA = OB
$\because$ Diagonals of a rectangle bisect each other
$\Rightarrow \angle OBA=\angle OAB={35}^{\circ }$ (As the angles opposite to equal sides are equal)

Applying exterior angle property in $\Delta$AOB
$\angle AOD=\angle OBA+\angle OAB$
$\angle AOD=35°+35°$
$\angle AOD=70°$