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