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The diagonals of a rectangle are inclined to one side of the rectangle at 25°. The acute angle formed between the diagonals is:
  • a)
    25°
  • b)
    50°
  • c)
    55°
  • d)
    40°
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The diagonals of a rectangle are inclined to one side of the rectangle...
Figure:

Calculation:
As the diagonals of a rectangle intersect each other,
⇒ AO = OB
⇒ ∠OBA = ∠OAB = 25° [∵ Angle opposite to equal side are equal]
By angle sum property in ΔAOB,
⇒ ∠AOB + ∠OAB + ∠OBA = 180°
⇒ ∠AOB + 25° + 25° = 180°
⇒ ∠AOB = 130°
By linear pair property,
⇒ ∠DOA + ∠AOB = 180°
⇒ ∠DOA + 130° = 180°
⇒ ∠DOA = 50°
∴ Both diagonals make 50° angle with each other.
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Most Upvoted Answer
The diagonals of a rectangle are inclined to one side of the rectangle...
Figure:

Calculation:
As the diagonals of a rectangle intersect each other,
⇒ AO = OB
⇒ ∠OBA = ∠OAB = 25° [∵ Angle opposite to equal side are equal]
By angle sum property in ΔAOB,
⇒ ∠AOB + ∠OAB + ∠OBA = 180°
⇒ ∠AOB + 25° + 25° = 180°
⇒ ∠AOB = 130°
By linear pair property,
⇒ ∠DOA + ∠AOB = 180°
⇒ ∠DOA + 130° = 180°
⇒ ∠DOA = 50°
∴ Both diagonals make 50° angle with each other.
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Community Answer
The diagonals of a rectangle are inclined to one side of the rectangle...
The diagonals of a rectangle are always equal in length and bisect each other. Additionally, the diagonals of a rectangle are perpendicular to each other.

In a rectangle, the angle between the diagonal and one side of the rectangle is always 45 degrees. This means that the angle between the diagonal and the other side of the rectangle is also 45 degrees.

Since the diagonals of a rectangle are perpendicular to each other, the angle between one diagonal and one side of the rectangle must be 90 degrees. Therefore, it is not possible for the diagonals of a rectangle to be inclined to one side of the rectangle at 25 degrees.
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The diagonals of a rectangle are inclined to one side of the rectangle at 25°. The acute angle formed between the diagonals is:a)25°b)50°c)55°d)40°Correct answer is option 'B'. Can you explain this answer?
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