If the angle of a quadrilateral are equal, prove that it is a rectangle.

Suppose there is a quadrilateral ABCD.

Let ∠A = ∠B = ∠C = ∠D = x

So, ∠A = ∠C and ∠B = ∠D (Opposite angles are equal)

∴ ABCD is a parallelogram.

Since, sum of angles in a quadrilateral = 360°

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ x + x + x + x = 360°

⇒ 4x = 360°

x = $\dfrac{360°}{4}$

⇒ x = 90°.

∴ ∠A = ∠B = ∠C = ∠D = 90°.

Since, each angle = 90°,

Hence, proved that ABCD is a rectangle.