Question

A diagonal of a rectangle makes an angle of $25°$ with one side of the rectangle. The acute angle between the diagonals is

• A. $25°$
• B. $40°$
• C. $50°$
• D. $55°$

Answer 1

The correct option is C $50°$



Let’s assume $\angle OCD=25°$ [Given that a diagonal makes an angle of 25° with a side of the rectangle]
We know that the diagonals of a rectangle bisect each other.
So,
$OC=\frac{1}{2}AC$
$OD=\frac{1}{2}BD$
$AC=BD$ [Diagonals of a rectangle are equal]
Therefore, $OC=OD$.
So, $OCD$ is forming an isosceles triangle.
Thus, $\angle ODC=\angle OCD=25°$ [Angles opposite to equal sides are equal]
Now, in the triangle $OCD,\angle BOC$ is an exterior angle.
So, we have,
$\angle BOC=\angle OCD+\angle ODC$ [Exterior angle is equal to the sum of opposite interior angles]
$\angle BOC=25°+25°=50°$
Thus, $\angle AOB=180°-\angle BOC=180°-50°=130°$
Therefore, the acute angle between the diagonals is $50°$.
So, the correct answer is option (c).