Question

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

विकल्प

• 55º

• 50º

• 40º

• 25º

Answer 1

A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between the diagonals is 50º.

Explanation:

Let ABCD be a rectangle, where ∠CAB = 25°.

We know, diagonals of a rectangle are equal in length.

∴ AC = BD

⇒ `1/2 AC = 1/2 BD`  ...[Dividing both sides by 2]

⇒ OA = OB   ...[Since, O is the mid-point of AC and BD]

⇒ ∠2 = ∠1  ...[Angles opposite to equal sides are equal]

⇒ ∠2 = 25°

Now, ∠3 = ∠1 + ∠2  ...[Exterior angle is equal to the sum of two opposite interior angles]

= 25° + 25°

= 50°

Hence, the acute angle between the diagonals is 50°.