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

1. 55°

2. 50°

3. 40°

4. 25°

From figure,

In △OBC,

OB = OC (Since diagonals bisect each other)

∠OCB = ∠OBC = 25°

⇒ ∠OBC + ∠OCB + ∠BOC = 180°

⇒ 25° + 25° + ∠BOC = 180°

⇒ ∠BOC = 130°.

Since, AC is a straight line,

⇒ ∠AOB + ∠BOC = 180°

⇒ ∠AOB = 180° - 130° = 50°.

Hence, Option 2 is the correct option.