Question

If all angles of a quadrilateral are congruent, then find their measures.

Answer 1

Given, all the angles of the quadrilateral are congruent that means, they are equal.

Let the angles of the quadrilateral be $x.$

We know, the sum of all four interior angles of a quadrilateral is ${360}^{\circ }.$ So,

$x+x+x+x+={360}^{\circ }$

$\Rightarrow 4x={360}^{\circ }$

$\Rightarrow x={90}^{\circ }$

Therefore, if all angles of a quadrilateral are congruent, then each angle will be equal to ${90}^{\circ }.$