Answer :

Given: Angle between a side of rectangle and its diagonal = 25°

Let the acute angle between diagonals be x

Now, we know that diagonals of a rectangle are equal in length i.e.,

AC = BD

Dividing both sides by 2,

⇒ 1/2AC = 1/2BD

⇒ OD = OC [∵ O is mid-point of AC and BD]

⇒ ∠y = 25° [∵ angles opposite to equal sides are equal]

Now we know that, exterior angle is equal to the sum of two opposite interior angles.

∴ ∠BOC = ∠ODC + ∠OCD

⇒ ∠x = ∠y + 25°

⇒ ∠x = 25° + 25°

⇒ ∠x = 50°

Hence, the acute angle between diagonals is 50°.

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