Question

One diagonal of a rectangle makes ${35}^o$ angle with larger side of rectangle. Find the obtuse angle between diagonals of the rectangle?

• A. ${70}^o$
• B. ${55}^o$
• C. ${110}^o$
• D. ${90}^o$

Answer 1

The correct option is C ${110}^o$


Let the rectangle be $ABCD$.

The diagonal $AC$ makes angle ${35}^o$ with side $AB$ of the rectangle.

Now we have to find out the value of angle $\angle AOB$ as this is the obtuse angle of intersection of diagonals when diagonals are intersecting at point $O$

Now, we know the diagonals of rectangles are equal and bisect each other.
So, $AC=BD$
and $AO=CO=OB=OD$

So, in $△AOB$
$AO=BO$
$\Rightarrow \angle OBA=\angle OAB\text{(angle opposite to equal sides are equal in triangle)}$
So, $\angle OBA={35}^o$

Now, by angle sum property of a triangle,
$\angle OAB+\angle OBA+\angle AOB={180}^o$
${35}^o+{35}^o+\angle AOB={180}^o$
${70}^o+\angle AOB={180}^o$
$\angle AOB={180}^o-{70}^o$
$\angle AOB={110}^o$

Hence, obtuse angle made by the intersection of diagonals of the rectangle is ${110}^o$.

hence, option $\left(c\right)$ correct.