Question

Question 5
All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?

Answer 1

We know that sum of all angles in a quadrilateral is ${360}^{\circ }$.

If ABCD is a quadrilateral.

$\angle A+\angle B+\angle C+\angle D={360}^{\circ }$

But it is given all angles are equal.

$\therefore \angle A=\angle B=\angle C=\angle D$

$\therefore$ $\angle A+\angle A+\angle A+\angle A={360}^{\circ }$

$\Rightarrow 4\angle A={360}^{\circ }$

$\therefore \angle A={90}^{\circ }$.

So, all angles of a quadrilateral are ${90}^{\circ }$.

Hence, given quadrilateral is a Rectangle or a Square.