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Mathematics

The angles of a quadrilateral are equal. Prove that the quadrilateral is a rectangle.

Rectilinear Figures

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Answer

Let ∠A = ∠B = ∠C = ∠D = x°

Sum of all angles in a quadrilateral is 360°.

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ x° + x° + x° + x° = 360°

⇒ 4x° = 360°

⇒ x° = 360°4\dfrac{360°}{4}

⇒ x° = 90°

Since, all angles of the quadrilateral are 90°, it follows that the quadrilateral is a rectangle.

Hence, the quadrilateral is a rectangle.

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