Question

A diagonal of a rectangle is inclined to one side of the rectangle at $25º$. The acute angle between the diagonals is

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

Answer 1

The correct option is B

$50º$

Step 1: Finding the value of $y$.

According to the given details,

A diagonal of a rectangle is inclined to one side of the rectangle at $25º$

So the angle between a side of the rectangle and its diagonal is $25º$

Let us assume the acute angle between diagonals to be $=\angle \mathrm{BOC}=x$

And also let $\angle \mathrm{ODC}=y$

We know that the diagonals of a rectangle are equal in length

$\mathrm{AC}=\mathrm{BD}$

On dividing R.H.S. and L.H.S. by $2$,

$\Rightarrow \frac{1}{2}\mathrm{AC}=\frac{1}{2}\mathrm{BD}$

Since $\mathrm{O}$ is the mid-point of $\mathrm{AC}$ and $\mathrm{BD}$

$\Rightarrow \mathrm{OD}=\mathrm{OC}$

Since angles opposite to equal sides are equal

$\Rightarrow \angle \mathrm{y}=25°$

Step 2: Finding the value of $x$.

Applying exterior angle property in triangle $\mathrm{ODC}$,

$$\begin{gathered} \angle \mathrm{BOC}=\angle \mathrm{ODC}+\angle \mathrm{OCD} \\ \Rightarrow \angle \mathrm{x}=\angle \mathrm{y}+25° \\ \Rightarrow \angle \mathrm{x}=25°+25° \\ \Rightarrow \angle \mathrm{x}=50° \end{gathered}$$

Hence, the acute angle between diagonals is $50º$.