Question

1. A diagonal of a rectangle is inclined to one side of the rectangle at
25°. The obtuse angle between the diagonals is
a ) 135°
b) 130°
c)140°
d)125°
​

Answer 1

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.