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

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Solution

In ∆AOB,
∠OAB + ∠ABO + ∠AOB = 180°
⇒ 25° + 25° + ∠AOB = 180°
⇒ ∠AOB + 50° = 180°
⇒ ∠AOB = 180° − 50°
⇒ ∠AOB = 130° which is an obtuse angle

Now, ∠AOB + ∠AOD = 180° (angles on a straight line)
⇒ 130° + ∠AOD = 180°
⇒ ∠AOD = 180° − 130°
⇒ ∠AOD = 50° which is an acute angle

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

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