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Question
A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between the diagonals is ______.
Options
55º
50º
40º
25º
Solution
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°.
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