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Question
If three angles of a quadrilateral are 90° each, show that the given quadrilateral is a rectangle.
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Solution
The given quadrilateral ABCD will be a rectangle, if its each angle is 90°
Since, the sum of interior angles of a quadrilateral is 360°.
∴∠A +∠B + ∠C + ∠D = 360°
⇒ 90° + 90° + 90° + ∠D = 360°
⇒ 270° + ∠D = 360°
⇒ ∠D = 360° – 270°
⇒ ∠D = 90°
Since, each angle of the quadrilateral is 90°. ∴The given quadrilateral is a rectangle.
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