Mathematics
The diagonals of the rectangle ABCD intersect at O. If ∠OBC = 64°, then ∠OAB =
64°
32°
26°
36°
Rectilinear Figures
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Answer
In a rectangle all angles are equal to 90°.
∠ABC = ∠OBC + ∠ABO
90° = 64° + ∠ABO
∠ABO = 90° - 64°
∠ABO = 26°.
The diagonals of a rectangle are equal in length and bisect each other. This means :
⇒ AC = BD
⇒ AO = BO
In an isosceles triangle AOB, the angles opposite the equal sides are equal.
∠OAB = ∠ABO = 26°.
Hence, option 3 is the correct option.
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