Mathematics
A diagonal of a rectangle is inclined to one side of the rectangle at 25°. The acute angle between the diagonals is
55°
50°
40°
25°
Rectilinear Figures
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Answer
From figure,
In △OBC,
OB = OC (Since diagonals bisect each other)
∠OCB = ∠OBC = 25°
⇒ ∠OBC + ∠OCB + ∠BOC = 180°
⇒ 25° + 25° + ∠BOC = 180°
⇒ ∠BOC = 130°.
Since, AC is a straight line,
⇒ ∠AOB + ∠BOC = 180°
⇒ ∠AOB = 180° - 130° = 50°.
Hence, Option 2 is the correct option.
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