Question

A diagonal of a rectangle is inclined to one side of the rectangle at ${35}^{\circ }$. The acute angle between the diagonals is

• A. 35
• B. 60
• C. 70
• D. 80

Answer 1

The correct option is C

70

The angle to be found is the acute angle between diagonals BD and AC.
That is, $\angle AOD$ or $\angle BOC.$

Since diagonals of a rectangle are equal, we know that $AO=OB.$

Hence,
$\angle OBA=\angle OAB={35}^{\circ }$

So, $\angle AOB={180}^{\circ }-{35}^{\circ }-{35}^{\circ }={110}^{\circ }$
(By angle sum property of a triangle)

Thus, $\angle AOD={180}^{\circ }-{110}^{\circ }={70}^{\circ }$
(Angles on a straight line are supplementary)