# A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between the diagonals is (A) 55º (B) 50º (C) 40º (D) 25º

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See diagram.

OAD = 25 deg.

So ODA = 25 deg. from symmetry of a rectangle.

So AOD = 180 - 25 - 25 = 130 deg.

Hence, the acute angle between diagonals : 180 - 130 = 50 deg.

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OR,

OAD = 25 deg. So BAO = 90 - 25 = 65 deg.

Since ABO = BAO, it is also 65 deg.

Hence, BOA = 180 - 65 - 65 = 50 deg.

OAD = 25 deg.

So ODA = 25 deg. from symmetry of a rectangle.

So AOD = 180 - 25 - 25 = 130 deg.

Hence, the acute angle between diagonals : 180 - 130 = 50 deg.

=============================

OR,

OAD = 25 deg. So BAO = 90 - 25 = 65 deg.

Since ABO = BAO, it is also 65 deg.

Hence, BOA = 180 - 65 - 65 = 50 deg.