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Question
All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?
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Solution
We know that, sum of all angles in a quadrilateral is 360°.
If ABCD is a quadrilateral,
∠A + ∠B + ∠C + ∠D = 360° ...(i)
But it is given all angles are equal.
∠A = ∠B = ∠C = ∠D
From equation ...(i)
∠A + ∠A + ∠A + ∠A = 360°
⇒ 4∠A = 360°
∠A = 90°
So, all angles of a quadrilateral are 90°.
Hence, given quadrilateral is a rectangle.
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